TY  - JOUR
AU  - Bród, Dorota
TI  - On Some Combinatorial Properties of Balancing Split Quaternions
JF  - SYMMETRY (BASEL)
J2  - SYMMETRY-BASEL
VL  - 16
PY  - 2024
IS  - 3
SP  - 373
SN  - 2073-8994
DO  - 10.3390/sym16030373
UR  - https://m2.mtmt.hu/api/publication/34751939
ID  - 34751939
AB  - Quaternions and split quaternions are used in quantum physics, computer science, and in many areas of mathematics. In this paper, we define and study two new classes of split quaternions, namely balancing split quaternions and Lucas-balancing split quaternions. Moreover, well-known properties, e.g., Catalan, d’Ocagne, and Vajda identities, for these quaternions are also presented. We give matrix generators for balancing split quaternions and Lucas-balancing split quaternions, too.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Chimpanzo, J.
AU  - Otero-Espinar, M.V.
AU  - Borges, A.
AU  - Vasco, P.
AU  - Catarino, P.
TI  - Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers
JF  - ANNALES MATHEMATICAE SILESIANAE
J2  - ANN MATH SIL
VL  - 38
PY  - 2024
IS  - 0
SP  - 1
SN  - 0860-2107
DO  - 10.2478/amsil-2023-0022
UR  - https://m2.mtmt.hu/api/publication/34449635
ID  - 34449635
AB  - A new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Naik, Avaya
TI  - Ä New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"
JF  - INTERNATIONAL JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
J2  - INTERNATIONAL JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
VL  - 19
PY  - 2024
IS  - 1
SP  - 01
EP  - 10
PG  - 10
SN  - 1819-4966
DO  - 10.37622/IJCAM/19.1.2024.01-010
UR  - https://m2.mtmt.hu/api/publication/34746887
ID  - 34746887
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Akgül, Arzu
TI  - Initial Coefficient Estimates of Bi-Univalent Functions Linked with Balancing Coefficients
JF  - WSEAS TRANSACTIONS ON MATHEMATICS
J2  - WSEAS TRANS MATH
VL  - 22
PY  - 2023
SP  - 792
EP  - 797
PG  - 6
SN  - 1109-2769
DO  - 10.37394/23206.2023.22.87
UR  - https://m2.mtmt.hu/api/publication/34216276
ID  - 34216276
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Brod, Dorota
AU  - Szynal-Liana, Anetta
TI  - On Bihypernomials Related to Balancing and Chebyshev Polynomials
JF  - Azerbaijan Journal of Mathematics
J2  - Azerbaijan Journal of Mathematics
VL  - 13
PY  - 2023
IS  - 02
SP  - 200
EP  - 218
PG  - 19
SN  - 2218-6816
DO  - 10.59849/2218-6816.2023.2.200
UR  - https://m2.mtmt.hu/api/publication/34084181
ID  - 34084181
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hulku, S
AU  - Deveci, Ö
TI  - The Tribonacci-type balancing numbers and their applications
JF  - MATHEMATICA MORAVICA
J2  - MATH MORAV
VL  - 27
PY  - 2023
IS  - 1
SP  - 23
EP  - 35
PG  - 13
SN  - 1450-5932
UR  - https://m2.mtmt.hu/api/publication/33681052
ID  - 33681052
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hussen, Abdulmtalb
AU  - Illafe, Mohamed
TI  - Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials
JF  - MATHEMATICS
J2  - MATHEMATICS-BASEL
VL  - 11
PY  - 2023
IS  - 24
SP  - 4941
SN  - 2227-7390
DO  - 10.3390/math11244941
UR  - https://m2.mtmt.hu/api/publication/34443849
ID  - 34443849
AB  - In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a2 and a3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.
LA  - English
DB  - MTMT
ER  - 

TY  - CONF
AU  - JOSÉ, CHIMPANZO
AU  - PAULA, CATARINO
AU  - MARÍA, OTERO-ESPINAR
TI  - Some Identities for Balancing and Lucas-Balancing Numbers in Bidimensional version
T2  - IV. International Conference on Mathematics and Its Applications in Science and Engineering (ICMASE 2023)
PY  - 2023
SP  - 17
EP  - 18
PG  - 2
UR  - https://m2.mtmt.hu/api/publication/34093945
ID  - 34093945
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Mehraban, Elahe
AU  - Hashemi, Mansour
TI  - Coding theory on the generalized balancing sequence
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 29
PY  - 2023
IS  - 3
SP  - 503
EP  - 524
PG  - 22
SN  - 1310-5132
DO  - 10.7546/nntdm.2023.29.3.503-524
UR  - https://m2.mtmt.hu/api/publication/34080969
ID  - 34080969
AB  - In this paper, we introduce the generalized balancing sequence and its matrix. Then by using the generalized balancing matrix, we give a coding and decoding method.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
TI  - CERTAIN IDENTITIES INVOLVING k-BALANCING AND k-LUCAS-BALANCING NUMBERS VIA MATRICES
JF  - ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS
J2  - ACTA MATH ACAD PAEDAG NYÍREGYH
VL  - 34
PY  - 2023
SP  - 120
EP  - 130
PG  - 11
SN  - 0866-0174
UR  - https://m2.mtmt.hu/api/publication/34080968
ID  - 34080968
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Sari, S
AU  - Gozeri, GK
TI  - b3-subbalancing and b3-Lucas subbalancing numbers
JF  - FILOMAT
J2  - FILOMAT
VL  - 37
PY  - 2023
IS  - 22
SP  - 7623
EP  - 7639
PG  - 17
SN  - 0354-5180
DO  - 10.2298/FIL2322623S
UR  - https://m2.mtmt.hu/api/publication/33871543
ID  - 33871543
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
AU  - Turkmen, Esra Zeynep
TI  - Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 29
PY  - 2023
IS  - 4
SP  - 682
EP  - 694
PG  - 13
SN  - 1310-5132
DO  - 10.7546/nntdm.2023.29.4.682
UR  - https://m2.mtmt.hu/api/publication/34591683
ID  - 34591683
AB  - In this work, the general terms of almost balancers, almost cobalancers, almost Lucasbalancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers. Later some relations on all almost balancing numbers and all almost balancers are obtained. Further the general terms of all balancing numbers, Pell numbers and Pell-Lucas number are determined in terms of almost balancers, almost Lucasbalancers, almost cobalancers and almost Lucas-cobalancers of first and second type.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Behera, A
AU  - Ray, PK
TI  - On the Properties of Balancing and Lucas-Balancing p-Numbers
JF  - IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS
J2  - IRAN J MATH SCI INFORM
VL  - 17
PY  - 2022
IS  - 2
SP  - 147
EP  - 163
PG  - 17
SN  - 1735-4463
DO  - 10.52547/ijmsi.17.2.147
UR  - https://m2.mtmt.hu/api/publication/33121096
ID  - 33121096
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bród, Dorota
AU  - Szynal-Liana, Anetta
AU  - Włoch, Iwona
TI  - Two generalizations of dual-complex Lucas-balancing numbers
JF  - ACTA UNIVERSITATIS SAPIENTIAE MATHEMATICA
J2  - ACTA UNIV SAPIENTIAE MATH
VL  - 14
PY  - 2022
IS  - 2
SP  - 220
EP  - 230
PG  - 11
SN  - 1844-6094
DO  - 10.2478/ausm-2022-0014
UR  - https://m2.mtmt.hu/api/publication/33582605
ID  - 33582605
AB  - In this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities.
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Mokrani, N
TI  - Variations sur les systèmes d’équations aux différences autonomes
PY  - 2022
UR  - https://m2.mtmt.hu/api/publication/33124032
ID  - 33124032
LA  - French
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Soykan, Yüksel
TI  - Generalized Edouard Numbers
JF  - International Journal of Advances in Applied Mathematics and Mechanics
J2  - International Journal of Advances in Applied Mathematics and Mechanics
VL  - 9
PY  - 2022
IS  - 3
SP  - 41
EP  - 52
PG  - 12
SN  - 2347-2529
UR  - https://m2.mtmt.hu/api/publication/32760449
ID  - 32760449
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Soykan, Yüksel
AU  - Tasdemir, Erkan
AU  - Dikmen, Can Murat
TI  - On the sum of the cubes of generalized balancing numbers. The sum formula n∑k=0xkW3mk+j
TS  - The sum formula n∑k=0xkW3mk+j
JF  - Open Journal of Mathematical Sciences
J2  - Open J. Math. Sci.
VL  - 6
PY  - 2022
IS  - 1
SP  - 152
EP  - 167
PG  - 16
SN  - 2616-4906
UR  - https://m2.mtmt.hu/api/publication/32922417
ID  - 32922417
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Sriram, S
AU  - Veeramallan, P
TI  - Generalized bi-periodic balancing numbers
JF  - ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES
J2  - ADV APPL MATH SCI
VL  - 21
PY  - 2022
IS  - 8
SP  - 4515
EP  - 4522
PG  - 8
SN  - 0974-6803
UR  - https://m2.mtmt.hu/api/publication/32930170
ID  - 32930170
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, A
AU  - Erdem, A
TI  - General terms of all almost balancing numbers of first and second type
JF  - COMMUNICATIONS IN MATHEMATICS
J2  - COMMUN MATH
VL  - 31
PY  - 2022
IS  - 1
EP  - 167
SN  - 1804-1388
DO  - 10.46298/cm.10318
UR  - https://m2.mtmt.hu/api/publication/33256522
ID  - 33256522
AB  - In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first and second type. We also set a correspondence between all almost balancing numbers of first and second type and Pell numbers. © 2023 Ahmet Tekcan and Alper Erdem.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
AU  - Yıldız, Meryem
TI  - Almost balcobalancing numbers
JF  - ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA
J2  - ANN UNIV SCI BP R EÖTVÖS NOM SECT COMPUT
VL  - 53
PY  - 2022
SP  - 71
EP  - 83
PG  - 13
SN  - 0138-9491
UR  - https://m2.mtmt.hu/api/publication/33298436
ID  - 33298436
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Amrouche, Said
TI  - Modelisátion de suites récurrentes linéaires par des triangles arithmétiques
PY  - 2021
UR  - https://m2.mtmt.hu/api/publication/32302173
ID  - 32302173
LA  - French
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bartz, Jeremiah
AU  - Dearden, Bruce
AU  - Iiams, Joel E.
TI  - Classes of gap balancing numbers
JF  - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
J2  - ROCKY MT J MATH
VL  - 51
PY  - 2021
IS  - 2
SP  - 399
EP  - 411
PG  - 13
SN  - 0035-7596
DO  - 10.1216/rmj.2021.51.399
UR  - https://m2.mtmt.hu/api/publication/32103423
ID  - 32103423
LA  - English
DB  - MTMT
ER  - 

TY  - CONF
AU  - Elahe, Mehraban
AU  - Mansour, Hashemi
TI  - Coding theory on the generalized balancing sequence
T2  - The 51th Annual Iranian Mathematics Conference
PY  - 2021
SP  - EMMH
PG  - 4
UR  - https://m2.mtmt.hu/api/publication/31898063
ID  - 31898063
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
AU  - Herendi, Orsolya
TI  - Polynomial values of surface point counting polynomials
JF  - INTERNATIONAL JOURNAL OF NUMBER THEORY
J2  - INT J NUMBER THEORY
VL  - 17
PY  - 2021
IS  - 1
SP  - 15
EP  - 32
PG  - 18
SN  - 1793-0421
DO  - 10.1142/S1793042121500020
UR  - https://m2.mtmt.hu/api/publication/31620931
ID  - 31620931
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Prasad, B
TI  - Coding theory based on balancing polynomials
JF  - CONTROL AND CYBERNETICS
J2  - CONTROL CYBERN
VL  - 50
PY  - 2021
IS  - 2
SP  - 335
EP  - 346
PG  - 12
SN  - 0324-8569
UR  - https://m2.mtmt.hu/api/publication/32770372
ID  - 32770372
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Soykan, Yüksel
AU  - Ta̧sdemir, Erkan
AU  - Dikmen, Can Murat
TI  - A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$
JF  - Journal of Innovative Applied Mathematics and Computational Sciences
J2  - JIAMCS
VL  - 1
PY  - 2021
IS  - 1
SP  - 16
EP  - 30
PG  - 15
SN  - 2773-4196
UR  - https://m2.mtmt.hu/api/publication/32682524
ID  - 32682524
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, A
AU  - Aydin, S
TI  - On t-Balancers, t-Balancing Numbers and Lucas t-Balancing Numbers
JF  - LIBERTAS MATHEMATICA
J2  - LIBERTAS MATHEMATICA
VL  - 41
PY  - 2021
IS  - 1
SP  - 37
EP  - 51
PG  - 15
SN  - 0278-5307
UR  - https://m2.mtmt.hu/api/publication/33269360
ID  - 33269360
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
AU  - Yildiz, Meryem
TI  - Balcobalancing numbers and balcobalancers
JF  - CREATIVE MATHEMATICS AND INFORMATICS
J2  - CREAT MATH INFORM
VL  - 30
PY  - 2021
IS  - 2
SP  - 203
EP  - 222
PG  - 20
SN  - 1584-286X
DO  - 10.37193/CMI.2021.02.11
UR  - https://m2.mtmt.hu/api/publication/32367186
ID  - 32367186
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
TI  - k-Almost Balancing Numbers
JF  - INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND STATISTICS
J2  - INT J APPL MAT STAT
VL  - 60
PY  - 2021
IS  - 3
SP  - 82
EP  - 89
PG  - 8
SN  - 0973-1377
UR  - https://m2.mtmt.hu/api/publication/32328454
ID  - 32328454
AB  - In this work, we determine the general terms of k-almost balancing numbers and k-almost Lucas-balancing numbers of first and second type in terms of balancing and Lucas-balancing numbers for some integer k >= 1.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ahmet, Tekcan
AU  - Meryem, Yıldız
TI  - Balcobalancing Numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 25
PY  - 2020
IS  - 1
SN  - 1310-5132
UR  - https://m2.mtmt.hu/api/publication/31634000
ID  - 31634000
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bartz, Jeremiah
AU  - Dearden, Bruce
AU  - Iiams, Joel
TI  - Counting families of generalized balancing numbers
JF  - AUSTRALASIAN JOURNAL OF COMBINATORICS
J2  - AUSTRALAS J COMBIN
VL  - 77
PY  - 2020
IS  - 3
SP  - 318
EP  - 325
PG  - 8
SN  - 1034-4942
UR  - https://m2.mtmt.hu/api/publication/31362476
ID  - 31362476
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bród, Dorota
AU  - Szynal-Liana, Anetta
AU  - Włoch, Iwona
TI  - Two Generalizations of Dual-Hyperbolic Balancing Numbers
JF  - SYMMETRY (BASEL)
J2  - SYMMETRY-BASEL
VL  - 12
PY  - 2020
IS  - 11
SP  - 1866
SN  - 2073-8994
DO  - 10.3390/sym12111866
UR  - https://m2.mtmt.hu/api/publication/31664662
ID  - 31664662
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - GP, Krisna
AU  - SS, Pradhan
TI  - TRIANGULAR-LIKE NUMBERS WHICH ARE TRIANGULAR
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 57
PY  - 2020
IS  - 4
SP  - 356
EP  - 362
PG  - 7
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/31138058
ID  - 31138058
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Komatsu, T.
AU  - Panda, G.K.
TI  - On several kinds of sums of balancing numbers
JF  - ARS COMBINATORIA
J2  - ARS COMBINATORIA
VL  - 153
PY  - 2020
SP  - 127
EP  - 148
PG  - 22
SN  - 0381-7032
UR  - https://m2.mtmt.hu/api/publication/34183879
ID  - 34183879
AB  - The balancing numbers Bn (n = 0,1, • • •) are solutions of the binary recurrence Bn = 6Bn-i - Bn-2 (n > 2) with Bo = 0 and B\\ = 1. In this paper we show several relations about the sums of product of two balancing numbers of the type £m=o £fcm+r-Bfe(n-m)+r (fc > r > 0) and the alternating sum of reciprocal of balancing numbers -g^J j. Similar results are also obtained for Lucas-balancing numbers C« (n = 0,1,«• ♦), satisfying the binary recurrence Cn = 6Cn-i - Cn-2 (n > 2) with Co = 1 and C\\ = 3. Some binomial sums involving these numbers are also explored. © 2020 Charles Babbage Research Centre. All rights reserved.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Pradhan, S.S.
AU  - Panda, G.K.
TI  - Sums of balancing-like sequences with binomial coefficients
JF  - Proceedings of the Jangjeon Mathematical Society
J2  - Proceedings of the Jangjeon Mathematical Society
VL  - 23
PY  - 2020
IS  - 3
SP  - 421
EP  - 432
PG  - 12
SN  - 1598-7264
DO  - 10.17777/pjms2020.23.3.421
UR  - https://m2.mtmt.hu/api/publication/31793954
ID  - 31793954
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Rayaguru, S. G.
AU  - Panda, G. K.
TI  - A generalization to almost balancing and cobalancing numbers using triangular numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 26
PY  - 2020
IS  - 3
SP  - 135
EP  - 148
PG  - 14
SN  - 1310-5132
DO  - 10.7546/nntdm.2020.26.3.135-148
UR  - https://m2.mtmt.hu/api/publication/31611232
ID  - 31611232
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, Prasanta Kumar
TI  - A cryptography method based on hyperbolic balancing and Lucas-balancing functions
JF  - PROYECCIONES JOURNAL OF MATHEMATICS
J2  - PROYECCIONES J MATH
VL  - 39
PY  - 2020
IS  - 1
SP  - 135
EP  - 152
PG  - 18
SN  - 0716-0917
DO  - 10.22199/issn.0717-6279-2020-01-0009
UR  - https://m2.mtmt.hu/api/publication/31197695
ID  - 31197695
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tasci, Dursun
AU  - Sevgi, Emre
TI  - Bi-Periodic Balancing Numbers
JF  - JOURNAL OF SCIENCE AND ARTS
J2  - J SCI ARTS
VL  - 20
PY  - 2020
IS  - 1
SP  - 75
EP  - 84
PG  - 10
SN  - 1844-9581
UR  - https://m2.mtmt.hu/api/publication/31294916
ID  - 31294916
LA  - Hungarian
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tasci, Dursun
AU  - Sevgi, Emre
TI  - BI-PERIODIC BALANCING NUMBERS
JF  - JOURNAL OF SCIENCE AND ARTS
J2  - J SCI ARTS
PY  - 2020
IS  - 1
SP  - 75
EP  - 84
PG  - 10
SN  - 1844-9581
UR  - https://m2.mtmt.hu/api/publication/31738637
ID  - 31738637
AB  - In this paper, we introduce a new generalization of the balancing numbers which we call bi-periodic balancing numbers asb(n) = {6cb(n-1) - b(n-2), if n is even, n >= 2 6db(n-1) - b(n-2), if n is oddwith initial conditions b(0) = 0, b(1) = 1. We find the generating function for this sequence and produce a Binet's formula.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
AU  - Erdem, Alper
TI  - t-cobalancing numbers and t-cobalancers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 26
PY  - 2020
IS  - 1
SP  - 45
EP  - 58
PG  - 14
SN  - 1310-5132
DO  - 10.7546/nntdm.2020.26.1.45-58
UR  - https://m2.mtmt.hu/api/publication/31286436
ID  - 31286436
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Aldred, Rachel
AU  - Goel, Rahul
AU  - Woodcock, James
AU  - Goodman, Anna
TI  - Contextualising Safety in Numbers: a longitudinal investigation into change in cycling safety in Britain, 1991–2001 and 2001–2011
JF  - INJURY PREVENTION
J2  - INJURY PREV
VL  - 25
PY  - 2019
IS  - 3
SP  - 236
EP  - 241
PG  - 6
SN  - 1353-8047
DO  - 10.1136/injuryprev-2017-042498
UR  - https://m2.mtmt.hu/api/publication/34185177
ID  - 34185177
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Bertók, Csanád
TI  - Exponential Diophantine Equations and Representation Problems
PB  - Debreceni Egyetem
PY  - 2019
SP  - 135
UR  - https://m2.mtmt.hu/api/publication/30630689
ID  - 30630689
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Frontczak, Robert
TI  - Identities for generalized balancing numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 25
PY  - 2019
IS  - 2
SP  - 169
EP  - 180
PG  - 12
SN  - 1310-5132
DO  - 10.7546/nntdm.2019.25.2.169-180
UR  - https://m2.mtmt.hu/api/publication/30729832
ID  - 30729832
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Frontczak, Robert
TI  - On Balancing polynomials
JF  - APPLIED MATHEMATICAL SCIENCES
J2  - APPLIED MATHEMATICAL SCIENCES
VL  - 13
PY  - 2019
IS  - 2
SP  - 57
EP  - 66
PG  - 10
SN  - 1312-885X
DO  - 10.12988/ams.2019.812183
UR  - https://m2.mtmt.hu/api/publication/30404453
ID  - 30404453
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Kumar Ray, Prasanta
TI  - Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes
JF  - AIMS MATHEMATICS
J2  - AIMS MATH
VL  - 4
PY  - 2019
IS  - 2
SP  - 308
EP  - 315
PG  - 8
SN  - 2473-6988
DO  - 10.3934/math.2018.2.308
UR  - https://m2.mtmt.hu/api/publication/30625997
ID  - 30625997
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, Gopal Krishna
AU  - Pradhan, Sushree Sangeeta
TI  - TRIANGULAR-LIKE NUMBERS THAT ARE TRIANGULAR
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 57
PY  - 2019
IS  - 4
SP  - 356
EP  - 362
PG  - 7
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/30957746
ID  - 30957746
AB  - A balancing-like sequence is a recurrence sequence satisfying the recurrence relation x(n+ 1) = Ax n - x(n-1) with initial terms x 0 = 0 and x 1 = 1 and A > 2 is a positive integer. For any given A, the nth triangular-like number is defined as T-n (A) = x(n)center dot x(n+1)/A. All the triangular-like numbers corresponding to the balancing-like sequence with A = 4 are triangular numbers. However, no other balancing-like sequence enjoys this property.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, A
TI  - Sums and spectral norms of all almost balancing numbers
JF  - CREATIVE MATHEMATICS AND INFORMATICS
J2  - CREAT MATH INFORM
VL  - 28
PY  - 2019
IS  - 2
SP  - 203
EP  - 214
PG  - 12
SN  - 1584-286X
UR  - https://m2.mtmt.hu/api/publication/30918070
ID  - 30918070
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
TI  - Almost balancing, triangular and square triangular numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 25
PY  - 2019
IS  - 1
SP  - 108
EP  - 121
PG  - 14
SN  - 1310-5132
DO  - 10.7546/nntdm.2019.25.1.108-121
UR  - https://m2.mtmt.hu/api/publication/30957747
ID  - 30957747
AB  - In this work, we derive some new algebraic relations on all almost balancing numbers (of first and second type) and triangular (and also square triangular) numbers.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bertók, Csanád
AU  - Hajdu, Lajos
TI  - A Hasse-type principle for exponential Diophantine equations over number fields and its applications
JF  - MONATSHEFTE FUR MATHEMATIK
J2  - MONATSH MATH
VL  - 187
PY  - 2018
IS  - 3
SP  - 425
EP  - 436
PG  - 12
SN  - 0026-9255
DO  - 10.1007/s00605-018-1169-8
UR  - https://m2.mtmt.hu/api/publication/3424357
ID  - 3424357
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Dutta, U.K.
AU  - Pradhan, S.S.
AU  - Ray, P.K.
TI  - Regularized products over balancing and lucas-balancing numbers
JF  - INDIAN JOURNAL OF MATHEMATICS
J2  - INDIAN J MATH
VL  - 60
PY  - 2018
IS  - 2
SP  - 171
EP  - 179
PG  - 9
SN  - 0019-5324
UR  - https://m2.mtmt.hu/api/publication/30325980
ID  - 30325980
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Frontczak, Robert
TI  - Sums of Balancing and Lucas-Balancing numbers with binomial coefficients
JF  - INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS
J2  - INT J MATH ANAL
VL  - 12
PY  - 2018
IS  - 12
SP  - 585
EP  - 594
PG  - 10
SN  - 1312-8876
DO  - 10.12988/ijma.2018.81067
UR  - https://m2.mtmt.hu/api/publication/30331624
ID  - 30331624
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, G.K.
AU  - Komatsu, T.
AU  - Davala, R.K.
TI  - Reciprocal sums of sequences involving balancing and lucas-balancing numbers
JF  - MATHEMATICAL REPORTS
J2  - MATH REP
VL  - 20
PY  - 2018
IS  - 2
SP  - 201
EP  - 214
PG  - 14
SN  - 1582-3067
UR  - https://m2.mtmt.hu/api/publication/30325981
ID  - 30325981
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Patel, KB
AU  - Irmak, N
AU  - Kumar, RP
AU  - Zaharescu, A
TI  - Incomplete balancing and lucas-balancing numbers
JF  - MATHEMATICAL REPORTS
J2  - MATH REP
PY  - 2018
SN  - 1582-3067
UR  - https://m2.mtmt.hu/api/publication/27285169
ID  - 27285169
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Rout, SS
AU  - Thangadurai, R
TI  - On l-th order gap balancing numbers
JF  - INTEGERS
J2  - INTEGERS
VL  - 18
PY  - 2018
SP  - 1
EP  - 12
PG  - 12
SN  - 1867-0652
UR  - https://m2.mtmt.hu/api/publication/27422453
ID  - 27422453
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Gozeri, Gul Karadeniz
AU  - Ozkoc, Arzu
AU  - Tekcan, Ahmet
TI  - SOME ALGEBRAIC RELATIONS ON BALANCING NUMBERS
JF  - UTILITAS MATHEMATICA
J2  - UTIL MAT
VL  - 103
PY  - 2017
SP  - 217
EP  - 236
PG  - 20
SN  - 0315-3681
UR  - https://m2.mtmt.hu/api/publication/26743899
ID  - 26743899
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ozkoc, Arzu
AU  - Tekcan, Ahmet
TI  - On k-balancing numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 23
PY  - 2017
IS  - 3
SP  - 38
EP  - 52
PG  - 15
SN  - 1310-5132
UR  - https://m2.mtmt.hu/api/publication/27307626
ID  - 27307626
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, AK
AU  - Panda, GK
TI  - CIRCULAR BALANCING NUMBERS
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 55
PY  - 2017
IS  - 4
SP  - 309
EP  - 314
PG  - 6
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/26981042
ID  - 26981042
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Patel, BK
AU  - Dutta, UK
AU  - Ray, PK
TI  - Period of balancing sequence modulo powers of balancing and Pell Numbers
JF  - ANNALES MATHEMATICAE ET INFORMATICAE
J2  - ANN MATH INFORM
VL  - 47
PY  - 2017
SP  - 177
EP  - 183
PG  - 7
SN  - 1787-5021
UR  - https://m2.mtmt.hu/api/publication/27016948
ID  - 27016948
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
TI  - Balancing Polynomials and Their Derivatives
JF  - UKRAINIAN MATHEMATICAL JOURNAL
J2  - UKR MATH J
VL  - 69
PY  - 2017
IS  - 4
SP  - 646
EP  - 663
PG  - 18
SN  - 0041-5995
DO  - 10.1007/s11253-017-1386-7
UR  - https://m2.mtmt.hu/api/publication/27018601
ID  - 27018601
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, Prasanta Kumar
AU  - Pradhan, Sushree Sangeeta
TI  - Greatest Common Divisors of Shifted Balancing Numbers
JF  - BOLETIM DA SOCIEDADE PARANAENSE DE MATEMATICA
J2  - B SOC PARAN MAT
VL  - 35
PY  - 2017
IS  - 3
SP  - 273
EP  - 283
PG  - 11
SN  - 0037-8712
DO  - 10.5269/bspm.v35i3.26093
UR  - https://m2.mtmt.hu/api/publication/26924019
ID  - 26924019
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, Prasanta Kumar
TI  - On the properties of k-balancing and k-Lucas-balancing numbers
JF  - ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA
J2  - ACTA COMM UNI TARTUENSIS MAT
VL  - 21
PY  - 2017
IS  - 2
SP  - 259
EP  - 274
PG  - 16
SN  - 1406-2283
DO  - 10.12697/ACUTM.2017.21.18
UR  - https://m2.mtmt.hu/api/publication/27319360
ID  - 27319360
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, Ahmet
AU  - Yazla, Aziz
TI  - t− BALANCING NUMBERS, PELL NUMBERS AND SQUARE TRIANGULAR NUMBERS
JF  - ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS
J2  - ACTA MATH ACAD PAEDAG NYÍREGYH
VL  - 33
PY  - 2017
IS  - 2
SP  - 133
EP  - 146
PG  - 14
SN  - 0866-0174
UR  - https://m2.mtmt.hu/api/publication/30641662
ID  - 30641662
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bijan, Kumar Patel
AU  - Prasanta, Kumar Ray
TI  - The period, rank and order of the sequence of balancing numbers modulo m
JF  - MATHEMATICAL REPORTS
J2  - MATH REP
VL  - 18
PY  - 2016
IS  - 3
SP  - 395
EP  - 401
PG  - 6
SN  - 1582-3067
UR  - https://m2.mtmt.hu/api/publication/25915936
ID  - 25915936
LA  - English
DB  - MTMT
ER  - 

TY  - GEN
AU  - Komatsu, T
AU  - Ray, PK
TI  - Higher-order identities for balancing numbers
PY  - 2016
PG  - 28
UR  - https://m2.mtmt.hu/api/publication/26063944
ID  - 26063944
LA  - English
DB  - MTMT
ER  - 

TY  - GEN
AU  - Komatsu, T
AU  - Panda, GK
TI  - On several kinds of sums of balancing numbers
PY  - 2016
UR  - https://m2.mtmt.hu/api/publication/26063941
ID  - 26063941
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Panda, Akshaya Kumar
TI  - Some Variants of the Balancing Sequence
PY  - 2016
UR  - https://m2.mtmt.hu/api/publication/30641660
ID  - 30641660
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Panda, Akshaya Kumar
TI  - Some Variants of the Balancing Sequence
PY  - 2016
SP  - 92
UR  - https://m2.mtmt.hu/api/publication/26656701
ID  - 26656701
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, Prasanta Kumar
AU  - Sahu, Juli
TI  - Generating functions for certain balancing and Lucas-balancing numbers
JF  - PALESTINE JOURNAL OF MATHEMATICS
J2  - PJM
VL  - 5
PY  - 2016
IS  - 2
SP  - 122
EP  - 129
PG  - 8
SN  - 2219-5688
UR  - https://m2.mtmt.hu/api/publication/25916005
ID  - 25916005
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, Prasanta Kumar
TI  - On the properties of k-balancing numbers
JF  - AIN SHAMS ENGINEERING JOURNAL
J2  - AIN SHAMS ENG J
VL  - 2016
PY  - 2016
IS  - 4
SP  - 395
EP  - 402
PG  - 8
SN  - 2090-4479
DO  - 10.1016/j.asej.2016.01.014
UR  - https://m2.mtmt.hu/api/publication/26161514
ID  - 26161514
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Swain, Sujata
AU  - Pratihary, Chidananda
AU  - Ray, Prasanta Kumar
TI  - Balancing and Lucas-Balancing Numbers and Their Application to Cryptography
JF  - Computer Engineering and Applications Journal
J2  - ComEngApp
VL  - 5
PY  - 2016
IS  - 1
SP  - 29
EP  - 36
PG  - 8
SN  - 2252-4274
UR  - https://m2.mtmt.hu/api/publication/30641659
ID  - 30641659
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ahmet, Tekcan
AU  - Merve, Tayat
AU  - Olajos, Péter
TI  - Balancing, Pell and square triangular functions
JF  - MISKOLC MATHEMATICAL NOTES
J2  - MISKOLC MATH NOTES
VL  - 16
PY  - 2015
IS  - 2
SP  - 1219
EP  - 1231
PG  - 13
SN  - 1787-2405
DO  - 10.18514/MMN.2015.1724
UR  - https://m2.mtmt.hu/api/publication/3005637
ID  - 3005637
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Catarino, P
AU  - Campos, H
AU  - Vasco, P
TI  - On some identities for balancing and co-balancing numbers
JF  - ANNALES MATHEMATICAE ET INFORMATICAE
J2  - ANN MATH INFORM
VL  - 45
PY  - 2015
SP  - 11
EP  - 24
PG  - 14
SN  - 1787-5021
UR  - https://m2.mtmt.hu/api/publication/25916010
ID  - 25916010
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ozkoç, A
TI  - Tridiagonal Matrices via k-Balancing Number
JF  - BRITISH JOURNAL OF MATHEMATICS & COMPUTER SCIENCE
J2  - BRIT J MATH COMPUT SCI
VL  - 10
PY  - 2015
IS  - 4
SP  - 1
EP  - 11
PG  - 11
SN  - 2231-0851
DO  - 10.9734/BJMCS/2015/19014
UR  - https://m2.mtmt.hu/api/publication/25915946
ID  - 25915946
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, GK
AU  - Panda, AK
TI  - Almost balancing numbers
JF  - JOURNAL OF THE INDIAN MATHEMATICAL SOCIETY
J2  - J IND MATH SOC
VL  - 82
PY  - 2015
IS  - 3-4
SP  - 147
EP  - 156
PG  - 10
SN  - 0019-5839
UR  - https://m2.mtmt.hu/api/publication/25249321
ID  - 25249321
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, P.K.
TI  - Balancing and Lucas-balancing sums by matrix methods
JF  - MATHEMATICAL REPORTS
J2  - MATH REP
VL  - 17
PY  - 2015
IS  - 2
SP  - 225
EP  - 233
PG  - 9
SN  - 1582-3067
UR  - https://m2.mtmt.hu/api/publication/34183867
ID  - 34183867
AB  - The balancing number n and the balancer r are solution of a simple Diophantine equation 1 + 2 + ⋯ + (n - 1) = (n + 1) + (n + 2) + ⋯ + (n + r). It is well known that if n is balancing number, then 8n2 + 1 is a perfect square and its positive square root is called a Lucas-balancing number. There is another way to generate balancing numbers and their related number sequences through matrices. The matrix representation indeed, gives many known and new formulas for these numbers. In this paper, two special types of 2 × 2 matrices (Formula presented.) and (Formula presented.) are introduced to derive some balancing and Lucas-balancing sums. Also, these matrices are used to establish some new identities for balancing and Lucas-balancing numbers.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
AU  - Swain, S
TI  - On the Hadamard Product of Balancing Q^n_B Matrix and Balancing Q^(−n)_B Matrix
JF  - TWMS Journal of Applied and Engineering Mathematics
J2  - TWMS Journal of Applied and Engineering Mathematics
VL  - 5
PY  - 2015
IS  - 2
SP  - 201
EP  - 207
PG  - 7
SN  - 2146-1147
UR  - https://m2.mtmt.hu/api/publication/25426804
ID  - 25426804
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
AU  - Panda, GK
TI  - Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 21
PY  - 2015
SP  - 56
EP  - 63
PG  - 8
SN  - 1310-5132
UR  - https://m2.mtmt.hu/api/publication/26344638
ID  - 26344638
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Rout, S S
AU  - Panda, G K
TI  - k-Gap balancing numbers
JF  - PERIODICA MATHEMATICA HUNGARICA
J2  - PERIOD MATH HUNG
VL  - 70
PY  - 2015
IS  - 1
SP  - 109
EP  - 121
PG  - 13
SN  - 0031-5303
DO  - 10.1007/s10998-014-0067-7
UR  - https://m2.mtmt.hu/api/publication/25074764
ID  - 25074764
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Rout, S S
TI  - Some generalizations and properties of balancing numbers
PY  - 2015
SP  - 102
UR  - https://m2.mtmt.hu/api/publication/32195375
ID  - 32195375
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Sudhansu, Sekhar Rout
TI  - Some Generalizations and Properties of Balancing Numbers
PY  - 2015
SP  - 112
UR  - https://m2.mtmt.hu/api/publication/25915939
ID  - 25915939
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Belbachir, H
AU  - Szalay, László
TI  - Balancing in the direction (1,-1) in the Pascal triangle
JF  - ARMENIAN JOURNAL OF MATHEMATICS
J2  - ARMENIAN J MATH
VL  - 6
PY  - 2014
IS  - 1
SP  - 32
EP  - 41
PG  - 10
SN  - 1829-1163
UR  - https://m2.mtmt.hu/api/publication/2726012
ID  - 2726012
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Komatsu, T
AU  - Szalay, László
TI  - Balancing with binomial coefficients
JF  - INTERNATIONAL JOURNAL OF NUMBER THEORY
J2  - INT J NUMBER THEORY
VL  - 10
PY  - 2014
IS  - 7
SP  - 1729
EP  - 1742
PG  - 14
SN  - 1793-0421
DO  - 10.1142/S1793042114500523
UR  - https://m2.mtmt.hu/api/publication/2565342
ID  - 2565342
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, G K
AU  - Rout, S S
TI  - Periodicity of Balancing Numbers
JF  - ACTA MATHEMATICA HUNGARICA
J2  - ACTA MATH HUNG
VL  - 143
PY  - 2014
IS  - 2
SP  - 274
EP  - 286
PG  - 13
SN  - 0236-5294
DO  - 10.1007/s10474-014-0427-z
UR  - https://m2.mtmt.hu/api/publication/25074766
ID  - 25074766
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Prasanta, Kumar Ray
TI  - Balancing sequences of matrices with application to algebra of balancing numbers
JF  - NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
J2  - NOTES NUMBER THEORY DISCRETE MATH
VL  - 20
PY  - 2014
IS  - 1
SP  - 49
EP  - 58
PG  - 10
SN  - 1310-5132
UR  - https://m2.mtmt.hu/api/publication/24410363
ID  - 24410363
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, P K
TI  - Some congruences for balancing and Lucas-balancing numbers and their applications
JF  - INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY
J2  - INTEGERS: ELECT J COMB NUM THEORY
VL  - 2014
PY  - 2014
PG  - 8
SN  - 1553-1732
UR  - https://m2.mtmt.hu/api/publication/23696761
ID  - 23696761
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
AU  - Dial, GK
AU  - Patel, BK
TI  - Application of Some Recurrence Relations to Cryptography using Finite State Machine
JF  - INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND ELECTRONICS ENGINEERING
J2  - IJCSEE
VL  - 2
PY  - 2014
IS  - 4
SP  - 220
EP  - 223
PG  - 4
SN  - 2320-401X
UR  - https://m2.mtmt.hu/api/publication/24379873
ID  - 24379873
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
AU  - Parida, K
TI  - Generalization of Cassini formulas for balancing and Lucas-balancing numbers
JF  - MATEMATYCHNI STUDII
J2  - MATEMAT STUD
VL  - 42
PY  - 2014
IS  - 1
SP  - 9
EP  - 14
PG  - 6
SN  - 1027-4634
UR  - https://m2.mtmt.hu/api/publication/24379884
ID  - 24379884
AB  - The mathematical identity that connects three adjacent balancing numbers is well known under the name Cassini formula, and is used to establish many important identities involving balancing numbers and their related sequences. This article is an attempt to draw attention to some of the unusual properties of generalized balancing numbers, in particular, to the general- ized Cassini formula.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
TI  - Identities involving the terms of a balancing-like sequence via matrices
JF  - CASPIAN JOURNAL OF APPLIED MATHEMATICS ECOLOGY AND ECONOMICS
J2  - CASPIAN J APPL MATH ECOL ECON
VL  - 2
PY  - 2014
IS  - 1
SP  - 94
EP  - 100
PG  - 7
SN  - 1560-4055
UR  - https://m2.mtmt.hu/api/publication/24995801
ID  - 24995801
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tekcan, A
AU  - Tayat, M
AU  - Özbek, ME
TI  - The Diophantine Equation $8x^{2}-y^{2}+8x(1+t)+(2t+1)^{2}=0$ and $t-$Balancing Numbers
JF  - ISRN COMBINATORICS
J2  - ISRN COMBINATORICS
VL  - 2014
PY  - 2014
IS  - Article ID 897834
SP  - 1
EP  - 5
PG  - 5
SN  - 2090-8911
DO  - 10.1155/2014/897834
UR  - https://m2.mtmt.hu/api/publication/23744013
ID  - 23744013
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Liptai, Kálmán
TI  - (a,b)-type balancing numbers
JF  - SURIKAISEKIKENKYUSHO KOKYUROKU / RIMS KOKYUROKU
J2  - RIMS KOKYUROKU
VL  - 1874
PY  - 2013
SP  - 115
EP  - 124
PG  - 10
SN  - 1880-2818
UR  - https://m2.mtmt.hu/api/publication/3058935
ID  - 3058935
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Panda, GK
AU  - Rout, SS
TI  - Gap balancing numbers
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 51
PY  - 2013
IS  - 3
SP  - 239
EP  - 248
PG  - 10
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/23333064
ID  - 23333064
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Ray, PK
TI  - New identities for the common factors of balancing and lucas-balancing numbers
JF  - INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS
J2  - INT J PURE APPL MATH
VL  - 85
PY  - 2013
IS  - 3
SP  - 487
EP  - 494
PG  - 8
SN  - 1311-8080
DO  - 10.12732/ijpam.v85i3.5
UR  - https://m2.mtmt.hu/api/publication/25915997
ID  - 25915997
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Szalay, László
TI  - Balansz számok és általánosításaik
JF  - DIMENZIÓK: MATEMATIKAI KÖZLEMÉNYEK
J2  - DIMENZIÓK
VL  - 1
PY  - 2013
SP  - 11
EP  - 13
PG  - 3
SN  - 9789633590195
SN  - 2064-2172
UR  - https://m2.mtmt.hu/api/publication/2339000
ID  - 2339000
LA  - Hungarian
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Tengely, Szabolcs
TI  - Balancing numbers which are products of consecutive integers
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 83
PY  - 2013
IS  - 1-2
SP  - 197
EP  - 205
PG  - 9
SN  - 0033-3883
DO  - 10.5486/PMD.2013.5654
UR  - https://m2.mtmt.hu/api/publication/1962085
ID  - 1962085
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Dash, KK
AU  - Ota, RS
AU  - Dash, S
TI  - t-Balancing Numbers
JF  - INTERNATIONAL JOURNAL OF CONTEMPORARY MATHEMATICAL SCIENCES
J2  - INT J CONTEMP MATH SCI
VL  - 7
PY  - 2012
IS  - 41
SP  - 1999
EP  - 2012
PG  - 14
SN  - 1312-7586
UR  - https://m2.mtmt.hu/api/publication/22481124
ID  - 22481124
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - K K, Dash
AU  - R S, Ota
TI  - Sequence $t$-balancing numbers
JF  - INTERNATIONAL JOURNAL OF CONTEMPORARY MATHEMATICAL SCIENCES
J2  - INT J CONTEMP MATH SCI
VL  - 7
PY  - 2012
IS  - 47
SP  - 2305
EP  - 2310
PG  - 6
SN  - 1312-7586
UR  - https://m2.mtmt.hu/api/publication/23174366
ID  - 23174366
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Liptai, Kálmán
AU  - Olajos, Péter
TI  - About the equation $B_m^{(a,b)}=f(x)$
JF  - ANNALES MATHEMATICAE ET INFORMATICAE
J2  - ANN MATH INFORM
VL  - 40
PY  - 2012
SP  - 47
EP  - 55
PG  - 9
SN  - 1787-5021
UR  - https://m2.mtmt.hu/api/publication/2341471
ID  - 2341471
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Olajos, Péter
TI  - A (2,1) típusú balansz számokról
JF  - GÉP
J2  - GÉP
VL  - 63
PY  - 2012
IS  - 4
SP  - 59
EP  - 62
PG  - 4
SN  - 0016-8572
UR  - https://m2.mtmt.hu/api/publication/1976364
ID  - 1976364
LA  - Hungarian
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Behera, A
AU  - Liptai, Kálmán
AU  - Panda, G K
AU  - Szalay, László
TI  - Balancing with Fibonacci powers
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 49
PY  - 2011
IS  - 1
SP  - 28
EP  - 33
PG  - 6
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/1781112
ID  - 1781112
AB  - The Diophantine equation F1k + F2k + ⋯ + Fn-1k = Fn+1l + Fn+2l + ⋯ + Fn+rl in positive integers n,r,k,l with n ≥ 2 is studied where F n is the nth term of the Fibonacci sequence.
LA  - English
DB  - MTMT
ER  - 

TY  - THES
AU  - Liptai, Kálmán
TI  - Balansz számok általánosításai
PY  - 2011
UR  - https://m2.mtmt.hu/api/publication/21343670
ID  - 21343670
LA  - Hungarian
DB  - MTMT
ER  -