@article{MTMT:34449635,
	title = {Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/34449635},
	author = {Chimpanzo, J. and Otero-Espinar, M.V. and Borges, A. and Vasco, P. and Catarino, P.},
	doi = {10.2478/amsil-2023-0022},
	journal-iso = {ANN MATH SIL},
	journal = {ANNALES MATHEMATICAE SILESIANAE},
	volume = {38},
	unique-id = {34449635},
	issn = {0860-2107},
	abstract = {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.},
	year = {2024},
	eissn = {2391-4238},
	pages = {1},
	orcid-numbers = {Catarino, P./0000-0001-6917-5093}
}

@article{MTMT:35158769,
	title = {Some Results on Certain Supercobalancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/35158769},
	author = {Karadeniz-Gözeri, Gül and Sarı, Selin},
	doi = {10.3390/axioms13080523},
	journal-iso = {AXIOMS},
	journal = {AXIOMS},
	volume = {13},
	unique-id = {35158769},
	abstract = {In this work, supercobalancing numbers are considered and some properties of these numbers are investigated. In the first part of this work, it is shown that every supercobalancing number is also a subbalancer. More specifically, B3-supercobalancing numbers which have not been considered before within the scope of this subject are examined. All the solution classes of the Diophantine equation of B3-supercobalancing numbers are determined exactly.},
	year = {2024},
	eissn = {2075-1680},
	pages = {523},
	orcid-numbers = {Karadeniz-Gözeri, Gül/0000-0003-2258-8266; Sarı, Selin/0000-0002-1080-6513}
}

@article{MTMT:33681052,
	title = {The Tribonacci-type balancing numbers and their applications},
	url = {https://m2.mtmt.hu/api/publication/33681052},
	author = {Hulku, S and Deveci, Ö},
	journal-iso = {MATH MORAV},
	journal = {MATHEMATICA MORAVICA},
	volume = {27},
	unique-id = {33681052},
	issn = {1450-5932},
	year = {2023},
	pages = {23-35}
}

@article{MTMT:34080968,
	title = {CERTAIN IDENTITIES INVOLVING k-BALANCING AND k-LUCAS-BALANCING NUMBERS VIA MATRICES},
	url = {https://m2.mtmt.hu/api/publication/34080968},
	author = {Ray, PK},
	journal-iso = {ACTA MATH ACAD PAEDAG NYÍREGYH},
	journal = {ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS},
	volume = {34},
	unique-id = {34080968},
	issn = {0866-0174},
	year = {2023},
	eissn = {1786-0091},
	pages = {120-130}
}

@article{MTMT:34125146,
	title = {On k -Fibonacci numbers expressible as product of two Balancing or Lucas-Balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/34125146},
	author = {Rihane, S.E.},
	doi = {10.1007/s13226-023-00485-0},
	journal-iso = {INDIAN J PURE AP MAT},
	journal = {INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS},
	volume = {2023},
	unique-id = {34125146},
	issn = {0019-5588},
	abstract = {The Balancing number n and the balancer r are solution of the Diophantine equation 1 + 2 + ⋯ + (n- 1) = (n+ 1) + (n+ 2) + ⋯ + (n+ r) . It is well known that if n is balancing number, then 8 n2+ 1 is a perfect square and its positive square root is called a Lucas-Balancing number. Let k≥ 2 . A generalization of the well-known Fibonacci sequence is the k-Fibonacci sequences. For these sequence the first k terms are 0 , … , 0 , 1 and each term afterwards is the sum of the preceding k terms. In this manuscript, our main objective is to find all k-Fibonacci numbers which are the product of two Balancing or Lucas-Balancing numbers. © 2023, The Indian National Science Academy.},
	keywords = {REDUCTION METHOD; Linear form in logarithms; Balancing numbers; k-Fibonacci numbers; Lucas-balancing numbers},
	year = {2023},
	eissn = {0975-7465}
}

@misc{MTMT:34763090,
	title = {La relation entre les nombres de Cobalancing et systèmes d'équations aux différences},
	url = {https://m2.mtmt.hu/api/publication/34763090},
	author = {Romaissa, Kadri Boufenghour Amani},
	unique-id = {34763090},
	year = {2023}
}

@article{MTMT:33871543,
	title = {b3-subbalancing and b3-Lucas subbalancing numbers},
	url = {https://m2.mtmt.hu/api/publication/33871543},
	author = {Sari, S and Gozeri, GK},
	doi = {10.2298/FIL2322623S},
	journal-iso = {FILOMAT},
	journal = {FILOMAT},
	volume = {37},
	unique-id = {33871543},
	issn = {0354-5180},
	year = {2023},
	eissn = {2406-0933},
	pages = {7623-7639}
}

@article{MTMT:34591683,
	title = {Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers},
	url = {https://m2.mtmt.hu/api/publication/34591683},
	author = {Tekcan, Ahmet and Turkmen, Esra Zeynep},
	doi = {10.7546/nntdm.2023.29.4.682},
	journal-iso = {NOTES NUMBER THEORY DISCRETE MATH},
	journal = {NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS},
	volume = {29},
	unique-id = {34591683},
	issn = {1310-5132},
	abstract = {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.},
	keywords = {Balancing numbers; Pell numbers; Pell-Lucas numbers; Almost balancing numbers},
	year = {2023},
	eissn = {2367-8275},
	pages = {682-694}
}

@article{MTMT:34520421,
	title = {ON DUAL BICOMPLEX BALANCING AND LUCAS-BALANCING NUMBERS},
	url = {https://m2.mtmt.hu/api/publication/34520421},
	author = {UYSAL, MINE and ÖZKAN, ENGIN and SHANNON, ANTHONY G.},
	journal-iso = {J SCI ARTS},
	journal = {JOURNAL OF SCIENCE AND ARTS},
	volume = {23},
	unique-id = {34520421},
	issn = {1844-9581},
	year = {2023},
	eissn = {2068-3049},
	pages = {925-938}
}

@article{MTMT:32916151,
	title = {Jump sizes for polygonal balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/32916151},
	author = {Bartz, Jeremiah and Dearden, Bruce and Iiams, Joel},
	journal-iso = {AUSTRALAS J COMBIN},
	journal = {AUSTRALASIAN JOURNAL OF COMBINATORICS},
	volume = {83},
	unique-id = {32916151},
	issn = {1034-4942},
	year = {2022},
	eissn = {2202-3518},
	pages = {337-347}
}

@article{MTMT:32864193,
	title = {Polygonal Balancing Numbers I},
	url = {https://m2.mtmt.hu/api/publication/32864193},
	author = {Bartz, Jeremiah and Dearden, Bruce and Iiams, Joel},
	journal-iso = {INTEGERS: ELECT J COMB NUM THEORY},
	journal = {INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY},
	volume = {22},
	unique-id = {32864193},
	year = {2022},
	eissn = {1553-1732}
}

@article{MTMT:32852401,
	title = {A note of 2-distance balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/32852401},
	author = {Chinram, R. and Petchkaew, P. and Hangsawat, S.},
	journal-iso = {Int J Math Comp Sci},
	journal = {INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE},
	volume = {17},
	unique-id = {32852401},
	issn = {1814-0424},
	abstract = {In this paper, we define and examine the concept of 2-distance balancing numbers. Moreover, we investigate some properties of those numbers and their recurrence relation. Furthermore, we provide the generating functions and Binet formula for 2-distance balancing numbers. © 2022. All Rights Reserved.},
	keywords = {Generating functions; 2-distance balancing numbers; Perfect square},
	year = {2022},
	eissn = {1814-0432},
	pages = {135-142}
}

@article{MTMT:32760449,
	title = {Generalized Edouard Numbers},
	url = {https://m2.mtmt.hu/api/publication/32760449},
	author = {Soykan, Yüksel},
	journal-iso = {International Journal of Advances in Applied Mathematics and Mechanics},
	journal = {International Journal of Advances in Applied Mathematics and Mechanics},
	volume = {9},
	unique-id = {32760449},
	issn = {2347-2529},
	year = {2022},
	pages = {41-52}
}

@article{MTMT:32922417,
	title = {On the sum of the cubes of generalized balancing numbers. The sum formula n∑k=0xkW3mk+j},
	url = {https://m2.mtmt.hu/api/publication/32922417},
	author = {Soykan, Yüksel and Tasdemir, Erkan and Dikmen, Can Murat},
	journal-iso = {Open J. Math. Sci.},
	journal = {Open Journal of Mathematical Sciences},
	volume = {6},
	unique-id = {32922417},
	issn = {2616-4906},
	year = {2022},
	eissn = {2523-0212},
	pages = {152-167}
}

@article{MTMT:33256522,
	title = {General terms of all almost balancing numbers of first and second type},
	url = {https://m2.mtmt.hu/api/publication/33256522},
	author = {Tekcan, A and Erdem, A},
	doi = {10.46298/cm.10318},
	journal-iso = {COMMUN MATH},
	journal = {COMMUNICATIONS IN MATHEMATICS},
	volume = {31},
	unique-id = {33256522},
	issn = {1804-1388},
	abstract = {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.},
	keywords = {Balancing number; Pell number; almost balancing number},
	year = {2022},
	eissn = {2336-1298},
	pages = {167}
}

@article{MTMT:33298436,
	title = {Almost balcobalancing numbers},
	url = {https://m2.mtmt.hu/api/publication/33298436},
	author = {Tekcan, Ahmet and Yıldız, Meryem},
	journal-iso = {ANN UNIV SCI BP R EÖTVÖS NOM SECT COMPUT},
	journal = {ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA},
	volume = {53},
	unique-id = {33298436},
	issn = {0138-9491},
	year = {2022},
	pages = {71-83}
}

@mastersthesis{MTMT:32541599,
	title = {𝒕-Kobalans ve Lucas 𝒕-Kobalans Sayilari},
	url = {https://m2.mtmt.hu/api/publication/32541599},
	author = {Erdem, Alper},
	unique-id = {32541599},
	year = {2021}
}

@article{MTMT:32100889,
	title = {On -Fibonacci balancing and -Fibonacci Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/32100889},
	author = {Rihane, S.E.},
	doi = {10.15330/cmp.13.1.259-271},
	journal-iso = {CARPATH MATH PUB},
	journal = {CARPATHIAN MATHEMATICAL PUBLICATIONS},
	volume = {13},
	unique-id = {32100889},
	issn = {2075-9827},
	year = {2021},
	eissn = {2313-0210},
	pages = {259-271}
}

@article{MTMT:32682524,
	title = {A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$},
	url = {https://m2.mtmt.hu/api/publication/32682524},
	author = {Soykan, Yüksel and Ta̧sdemir, Erkan and Dikmen, Can Murat},
	journal-iso = {JIAMCS},
	journal = {Journal of Innovative Applied Mathematics and Computational Sciences},
	volume = {1},
	unique-id = {32682524},
	year = {2021},
	eissn = {2773-4196},
	pages = {16-30}
}

@article{MTMT:32367186,
	title = {Balcobalancing numbers and balcobalancers},
	url = {https://m2.mtmt.hu/api/publication/32367186},
	author = {Tekcan, Ahmet and Yildiz, Meryem},
	doi = {10.37193/CMI.2021.02.11},
	journal-iso = {CREAT MATH INFORM},
	journal = {CREATIVE MATHEMATICS AND INFORMATICS},
	volume = {30},
	unique-id = {32367186},
	issn = {1584-286X},
	year = {2021},
	eissn = {1843-441X},
	pages = {203-222}
}

@article{MTMT:32328454,
	title = {k-Almost Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/32328454},
	author = {Tekcan, Ahmet},
	journal-iso = {INT J APPL MAT STAT},
	journal = {INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND STATISTICS},
	volume = {60},
	unique-id = {32328454},
	issn = {0973-1377},
	abstract = {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.},
	keywords = {quadratic form; Pell equation; Balancing number; almost balancing number; cobalancing number},
	year = {2021},
	eissn = {0973-7545},
	pages = {82-89}
}

@article{MTMT:31634000,
	title = {Balcobalancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/31634000},
	author = {Ahmet, Tekcan and Meryem, Yıldız},
	journal-iso = {NOTES NUMBER THEORY DISCRETE MATH},
	journal = {NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS},
	volume = {25},
	unique-id = {31634000},
	issn = {1310-5132},
	year = {2020},
	eissn = {2367-8275}
}

@article{MTMT:34183879,
	title = {On several kinds of sums of balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/34183879},
	author = {Komatsu, T. and Panda, G.K.},
	journal-iso = {ARS COMBINATORIA},
	journal = {ARS COMBINATORIA},
	volume = {153},
	unique-id = {34183879},
	issn = {0381-7032},
	abstract = {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.},
	keywords = {Balancing numbers; Lucas-balancing numbers; reciprocal sums},
	year = {2020},
	pages = {127-148}
}

@article{MTMT:31644540,
	title = {Shift Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/31644540},
	author = {Rayaguru, S. G. and Panda, G. K. and Davala, R. K.},
	doi = {10.18311/jims/2020/24872},
	journal-iso = {J IND MATH SOC},
	journal = {JOURNAL OF THE INDIAN MATHEMATICAL SOCIETY},
	volume = {87},
	unique-id = {31644540},
	issn = {0019-5839},
	year = {2020},
	pages = {131}
}

@article{MTMT:31197695,
	title = {A cryptography method based on hyperbolic balancing and Lucas-balancing functions},
	url = {https://m2.mtmt.hu/api/publication/31197695},
	author = {Ray, Prasanta Kumar},
	doi = {10.22199/issn.0717-6279-2020-01-0009},
	journal-iso = {PROYECCIONES J MATH},
	journal = {PROYECCIONES JOURNAL OF MATHEMATICS},
	volume = {39},
	unique-id = {31197695},
	issn = {0716-0917},
	year = {2020},
	eissn = {0717-6279},
	pages = {135-152},
	orcid-numbers = {Ray, Prasanta Kumar/0000-0002-1208-8113}
}

@article{MTMT:31286436,
	title = {t-cobalancing numbers and t-cobalancers},
	url = {https://m2.mtmt.hu/api/publication/31286436},
	author = {Tekcan, Ahmet and Erdem, Alper},
	doi = {10.7546/nntdm.2020.26.1.45-58},
	journal-iso = {NOTES NUMBER THEORY DISCRETE MATH},
	journal = {NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS},
	volume = {26},
	unique-id = {31286436},
	issn = {1310-5132},
	year = {2020},
	eissn = {2367-8275},
	pages = {45-58}
}

@article{MTMT:30729832,
	title = {Identities for generalized balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/30729832},
	author = {Frontczak, Robert},
	doi = {10.7546/nntdm.2019.25.2.169-180},
	journal-iso = {NOTES NUMBER THEORY DISCRETE MATH},
	journal = {NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS},
	volume = {25},
	unique-id = {30729832},
	issn = {1310-5132},
	year = {2019},
	eissn = {2367-8275},
	pages = {169-180}
}

@article{MTMT:30625997,
	title = {Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes},
	url = {https://m2.mtmt.hu/api/publication/30625997},
	author = {Kumar Ray, Prasanta},
	doi = {10.3934/math.2018.2.308},
	journal-iso = {AIMS MATH},
	journal = {AIMS MATHEMATICS},
	volume = {4},
	unique-id = {30625997},
	year = {2019},
	eissn = {2473-6988},
	pages = {308-315}
}

@article{MTMT:30918070,
	title = {Sums and spectral norms of all almost balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/30918070},
	author = {Tekcan, A},
	journal-iso = {CREAT MATH INFORM},
	journal = {CREATIVE MATHEMATICS AND INFORMATICS},
	volume = {28},
	unique-id = {30918070},
	issn = {1584-286X},
	year = {2019},
	eissn = {1843-441X},
	pages = {203-214}
}

@article{MTMT:30957747,
	title = {Almost balancing, triangular and square triangular numbers},
	url = {https://m2.mtmt.hu/api/publication/30957747},
	author = {Tekcan, Ahmet},
	doi = {10.7546/nntdm.2019.25.1.108-121},
	journal-iso = {NOTES NUMBER THEORY DISCRETE MATH},
	journal = {NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS},
	volume = {25},
	unique-id = {30957747},
	issn = {1310-5132},
	abstract = {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.},
	keywords = {Balancing numbers; Triangular numbers; Almost balancing numbers; Square triangular numbers},
	year = {2019},
	eissn = {2367-8275},
	pages = {108-121}
}

@article{MTMT:30325980,
	title = {Regularized products over balancing and lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/30325980},
	author = {Dutta, U.K. and Pradhan, S.S. and Ray, P.K.},
	journal-iso = {INDIAN J MATH},
	journal = {INDIAN JOURNAL OF MATHEMATICS},
	volume = {60},
	unique-id = {30325980},
	issn = {0019-5324},
	year = {2018},
	pages = {171-179}
}

@article{MTMT:30380100,
	title = {A note on hybrid convolutions involving Balancing and Lucas-Balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/30380100},
	author = {Frontczak, Robert},
	doi = {10.12988/ams.2018.87111},
	journal-iso = {APPLIED MATHEMATICAL SCIENCES},
	journal = {APPLIED MATHEMATICAL SCIENCES},
	volume = {12},
	unique-id = {30380100},
	issn = {1312-885X},
	year = {2018},
	eissn = {1314-7552},
	pages = {1201-1208}
}

@article{MTMT:30331624,
	title = {Sums of Balancing and Lucas-Balancing numbers with binomial coefficients},
	url = {https://m2.mtmt.hu/api/publication/30331624},
	author = {Frontczak, Robert},
	doi = {10.12988/ijma.2018.81067},
	journal-iso = {INT J MATH ANAL},
	journal = {INTERNATIONAL JOURNAL OF MATHEMATICAL ANALYSIS},
	volume = {12},
	unique-id = {30331624},
	issn = {1312-8876},
	year = {2018},
	eissn = {1314-7579},
	pages = {585-594}
}

@article{MTMT:27161865,
	title = {On Pell, Pell-Lucas, and balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/27161865},
	author = {Karadeniz, Gözeri G},
	doi = {10.1186/s13660-017-1599-1},
	journal-iso = {J INEQUAL APPL},
	journal = {JOURNAL OF INEQUALITIES AND APPLICATIONS},
	volume = {2018},
	unique-id = {27161865},
	issn = {1025-5834},
	year = {2018},
	eissn = {1029-242X}
}

@article{MTMT:30325981,
	title = {Reciprocal sums of sequences involving balancing and lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/30325981},
	author = {Panda, G.K. and Komatsu, T. and Davala, R.K.},
	journal-iso = {MATH REP},
	journal = {MATHEMATICAL REPORTS},
	volume = {20},
	unique-id = {30325981},
	issn = {1582-3067},
	year = {2018},
	eissn = {1582-3067},
	pages = {201-214}
}

@article{MTMT:34183880,
	title = {Repdigits as products of consecutive balancing or Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/34183880},
	author = {Rayaguru, S.G. and Panda, G.K.},
	journal-iso = {FIBONACCI QUART},
	journal = {FIBONACCI QUARTERLY},
	volume = {56},
	unique-id = {34183880},
	issn = {0015-0517},
	abstract = {Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive-balancing or Lucas-balancing numbers. © 2018 The Fibonacci Association. All rights reserved.},
	year = {2018},
	eissn = {0015-0517},
	pages = {319-324}
}

@article{MTMT:30554457,
	title = {GAUSSIAN BALANCING NUMBERS AND GAUSSIAN LUCAS-BALANCING NUMBERS},
	url = {https://m2.mtmt.hu/api/publication/30554457},
	author = {Tasci, Dursun},
	journal-iso = {J SCI ARTS},
	journal = {JOURNAL OF SCIENCE AND ARTS},
	unique-id = {30554457},
	issn = {1844-9581},
	abstract = {In this study we define Gaussian balancing numbers and Gaussian Lucas-balancing numbers. Then we obtain Binet-like formulas, generating functions and some identities related with Gaussian balancing numbers and Gaussian Lucas-balancing numbers. Moreover, we give the new properties of Gaussian balancing numbers and Gaussian Lucas-balancing numbers in relation with balancing matrix formula.},
	keywords = {Balancing and Lucas-balancing numbers; Gaussian balancing numbers; Gaussian Lucas-balancing numbers},
	year = {2018},
	eissn = {2068-3049},
	pages = {661-666}
}

@article{MTMT:26743899,
	title = {SOME ALGEBRAIC RELATIONS ON BALANCING NUMBERS},
	url = {https://m2.mtmt.hu/api/publication/26743899},
	author = {Gozeri, Gul Karadeniz and Ozkoc, Arzu and Tekcan, Ahmet},
	journal-iso = {UTIL MAT},
	journal = {UTILITAS MATHEMATICA},
	volume = {103},
	unique-id = {26743899},
	issn = {0315-3681},
	year = {2017},
	pages = {217-236}
}

@book{MTMT:26661831,
	title = {Fibonacci Numbers and the Golden Section},
	url = {https://m2.mtmt.hu/api/publication/26661831},
	author = {Knott, Ron},
	publisher = {University of Surrey, Department of Mathematics},
	unique-id = {26661831},
	year = {2017}
}

@article{MTMT:26555445,
	title = {TRIANGULAR AND SQUARE TRIANGULAR NUMBERS INVOLVING GENERALIZED PELL NUMBERS},
	url = {https://m2.mtmt.hu/api/publication/26555445},
	author = {Ozkoc, Arzu and Tekcan, Ahmet and Gozeri, Gul Karadeniz},
	journal-iso = {UTIL MAT},
	journal = {UTILITAS MATHEMATICA},
	volume = {102},
	unique-id = {26555445},
	issn = {0315-3681},
	year = {2017},
	pages = {231-254}
}

@article{MTMT:27018601,
	title = {Balancing Polynomials and Their Derivatives},
	url = {https://m2.mtmt.hu/api/publication/27018601},
	author = {Ray, PK},
	doi = {10.1007/s11253-017-1386-7},
	journal-iso = {UKR MATH J},
	journal = {UKRAINIAN MATHEMATICAL JOURNAL},
	volume = {69},
	unique-id = {27018601},
	issn = {0041-5995},
	year = {2017},
	eissn = {1573-9376},
	pages = {646-663}
}

@article{MTMT:26924019,
	title = {Greatest Common Divisors of Shifted Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/26924019},
	author = {Ray, Prasanta Kumar and Pradhan, Sushree Sangeeta},
	doi = {10.5269/bspm.v35i3.26093},
	journal-iso = {B SOC PARAN MAT},
	journal = {BOLETIM DA SOCIEDADE PARANAENSE DE MATEMATICA},
	volume = {35},
	unique-id = {26924019},
	issn = {0037-8712},
	year = {2017},
	eissn = {2175-1188},
	pages = {273-283}
}

@article{MTMT:27319360,
	title = {On the properties of k-balancing and k-Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/27319360},
	author = {Ray, Prasanta Kumar},
	doi = {10.12697/ACUTM.2017.21.18},
	journal-iso = {ACTA COMM UNI TARTUENSIS MAT},
	journal = {ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA},
	volume = {21},
	unique-id = {27319360},
	issn = {1406-2283},
	year = {2017},
	eissn = {2228-4699},
	pages = {259-274}
}

@misc{MTMT:26063944,
	title = {Higher-order identities for balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/26063944},
	author = {Komatsu, T and Ray, PK},
	unique-id = {26063944},
	year = {2016}
}

@misc{MTMT:26063941,
	title = {On several kinds of sums of balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/26063941},
	author = {Komatsu, T and Panda, GK},
	unique-id = {26063941},
	year = {2016}
}

@misc{MTMT:26169994,
	title = {Higher-order identities for balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/26169994},
	author = {Komatsu, Takao and Ray, Prasanta Kumar},
	unique-id = {26169994},
	year = {2016}
}

@mastersthesis{MTMT:30641660,
	title = {Some Variants of the Balancing Sequence},
	url = {https://m2.mtmt.hu/api/publication/30641660},
	author = {Panda, Akshaya Kumar},
	unique-id = {30641660},
	year = {2016}
}

@mastersthesis{MTMT:26656701,
	title = {Some Variants of the Balancing Sequence},
	url = {https://m2.mtmt.hu/api/publication/26656701},
	author = {Panda, Akshaya Kumar},
	unique-id = {26656701},
	year = {2016}
}

@article{MTMT:26474133,
	title = {Certain diophantine equations involving balancing and Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/26474133},
	author = {Ray, P K},
	doi = {10.12697/ACUTM.2016.20.14},
	journal-iso = {ACTA COMM UNI TARTUENSIS MAT},
	journal = {ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA},
	volume = {20},
	unique-id = {26474133},
	issn = {1406-2283},
	year = {2016},
	eissn = {2228-4699},
	pages = {165-173}
}

@article{MTMT:26841986,
	title = {A trigonometry approach to balancing numbers and their related sequences},
	url = {https://m2.mtmt.hu/api/publication/26841986},
	author = {Ray, Prasanta Kumar},
	journal-iso = {Sigmae},
	journal = {Sigmae},
	volume = {5},
	unique-id = {26841986},
	issn = {2317-0840},
	year = {2016},
	eissn = {2317-0840},
	pages = {1-7}
}

@article{MTMT:25916005,
	title = {Generating functions for certain balancing and Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/25916005},
	author = {Ray, Prasanta Kumar and Sahu, Juli},
	journal-iso = {PJM},
	journal = {PALESTINE JOURNAL OF MATHEMATICS},
	volume = {5},
	unique-id = {25916005},
	issn = {2219-5688},
	year = {2016},
	pages = {122-129}
}

@article{MTMT:30641659,
	title = {Balancing and Lucas-Balancing Numbers and Their Application to Cryptography},
	url = {https://m2.mtmt.hu/api/publication/30641659},
	author = {Swain, Sujata and Pratihary, Chidananda and Ray, Prasanta Kumar},
	journal-iso = {ComEngApp},
	journal = {Computer Engineering and Applications Journal},
	volume = {5},
	unique-id = {30641659},
	issn = {2252-4274},
	year = {2016},
	eissn = {2252-5459},
	pages = {29-36}
}

@article{MTMT:26206952,
	title = {SOME ALGEBRAIC RELATIONS ON INTEGER SEQUENCES INVOLVING OBLONG AND BALANCING NUMBERS},
	url = {https://m2.mtmt.hu/api/publication/26206952},
	author = {Tekcan, Ahmet and Ozkoc, Arzu and Erasik, Meltem E},
	journal-iso = {ARS COMBINATORIA},
	journal = {ARS COMBINATORIA},
	volume = {128},
	unique-id = {26206952},
	issn = {0381-7032},
	year = {2016},
	pages = {11-31}
}

@article{MTMT:3005637,
	title = {Balancing, Pell and square triangular functions},
	url = {https://m2.mtmt.hu/api/publication/3005637},
	author = {Ahmet, Tekcan and Merve, Tayat and Olajos, Péter},
	doi = {10.18514/MMN.2015.1724},
	journal-iso = {MISKOLC MATH NOTES},
	journal = {MISKOLC MATHEMATICAL NOTES},
	volume = {16},
	unique-id = {3005637},
	issn = {1787-2405},
	year = {2015},
	eissn = {1787-2413},
	pages = {1219-1231}
}

@article{MTMT:25916010,
	title = {On some identities for balancing and co-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/25916010},
	author = {Catarino, P and Campos, H and Vasco, P},
	journal-iso = {ANN MATH INFORM},
	journal = {ANNALES MATHEMATICAE ET INFORMATICAE},
	volume = {45},
	unique-id = {25916010},
	issn = {1787-5021},
	year = {2015},
	eissn = {1787-6117},
	pages = {11-24}
}

@article{MTMT:34183867,
	title = {Balancing and Lucas-balancing sums by matrix methods},
	url = {https://m2.mtmt.hu/api/publication/34183867},
	author = {Ray, P.K.},
	journal-iso = {MATH REP},
	journal = {MATHEMATICAL REPORTS},
	volume = {17},
	unique-id = {34183867},
	issn = {1582-3067},
	abstract = {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.},
	keywords = {Balancing numbers; Balancers; Lucas-balancing numbers; Balancing matrices},
	year = {2015},
	eissn = {1582-3067},
	pages = {225-233}
}

@article{MTMT:25426804,
	title = {On the Hadamard Product of Balancing Q^n_B Matrix and Balancing Q^(−n)_B Matrix},
	url = {https://m2.mtmt.hu/api/publication/25426804},
	author = {Ray, PK and Swain, S},
	journal-iso = {TWMS Journal of Applied and Engineering Mathematics},
	journal = {TWMS Journal of Applied and Engineering Mathematics},
	volume = {5},
	unique-id = {25426804},
	issn = {2146-1147},
	year = {2015},
	eissn = {2146-1147},
	pages = {201-207}
}

@article{MTMT:25074764,
	title = {k-Gap balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/25074764},
	author = {Rout, S S and Panda, G K},
	doi = {10.1007/s10998-014-0067-7},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	volume = {70},
	unique-id = {25074764},
	issn = {0031-5303},
	year = {2015},
	eissn = {1588-2829},
	pages = {109-121}
}

@mastersthesis{MTMT:32195375,
	title = {Some generalizations and properties of balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/32195375},
	author = {Rout, S S},
	unique-id = {32195375},
	year = {2015}
}

@mastersthesis{MTMT:25915939,
	title = {Some Generalizations and Properties of Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/25915939},
	author = {Sudhansu, Sekhar Rout},
	unique-id = {25915939},
	year = {2015}
}

@article{MTMT:25074766,
	title = {Periodicity of Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/25074766},
	author = {Panda, G K and Rout, S S},
	doi = {10.1007/s10474-014-0427-z},
	journal-iso = {ACTA MATH HUNG},
	journal = {ACTA MATHEMATICA HUNGARICA},
	volume = {143},
	unique-id = {25074766},
	issn = {0236-5294},
	year = {2014},
	eissn = {1588-2632},
	pages = {274-286}
}

@article{MTMT:24379873,
	title = {Application of Some Recurrence Relations to Cryptography using Finite State Machine},
	url = {https://m2.mtmt.hu/api/publication/24379873},
	author = {Ray, PK and Dial, GK and Patel, BK},
	journal-iso = {IJCSEE},
	journal = {INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND ELECTRONICS ENGINEERING},
	volume = {2},
	unique-id = {24379873},
	issn = {2320-401X},
	year = {2014},
	eissn = {2320-4028},
	pages = {220-223}
}

@article{MTMT:25916022,
	title = {Some congruences for balancing and Lucas-balancing numbers and their applications},
	url = {https://m2.mtmt.hu/api/publication/25916022},
	author = {Ray, PK},
	journal-iso = {INTEGERS: ELECT J COMB NUM THEORY},
	journal = {INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY},
	volume = {14},
	unique-id = {25916022},
	year = {2014},
	eissn = {1553-1732}
}

@article{MTMT:26655718,
	title = {On the properties of Lucas-balancing numbers by matrix method},
	url = {https://m2.mtmt.hu/api/publication/26655718},
	author = {Ray, Prasanta Kumar},
	journal-iso = {Sigmae},
	journal = {Sigmae},
	volume = {3},
	unique-id = {26655718},
	issn = {2317-0840},
	year = {2014},
	eissn = {2317-0840},
	pages = {1-6}
}

@article{MTMT:3058935,
	title = {(a,b)-type balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/3058935},
	author = {Liptai, Kálmán},
	journal-iso = {RIMS KOKYUROKU},
	journal = {SURIKAISEKIKENKYUSHO KOKYUROKU / RIMS KOKYUROKU},
	volume = {1874},
	unique-id = {3058935},
	issn = {1880-2818},
	year = {2013},
	pages = {115-124}
}

@article{MTMT:23333064,
	title = {Gap balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/23333064},
	author = {Panda, GK and Rout, SS},
	journal-iso = {FIBONACCI QUART},
	journal = {FIBONACCI QUARTERLY},
	volume = {51},
	unique-id = {23333064},
	issn = {0015-0517},
	year = {2013},
	eissn = {0015-0517},
	pages = {239-248}
}

@article{MTMT:25915997,
	title = {New identities for the common factors of balancing and lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/25915997},
	author = {Ray, PK},
	doi = {10.12732/ijpam.v85i3.5},
	journal-iso = {INT J PURE APPL MATH},
	journal = {INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS},
	volume = {85},
	unique-id = {25915997},
	issn = {1311-8080},
	year = {2013},
	pages = {487-494}
}

@article{MTMT:26655691,
	title = {Factorizations of the negatively subscripted balancing and Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/26655691},
	author = {Ray, Prasanta Kumar},
	doi = {10.5269/bspm.v31i2.14263},
	journal-iso = {B SOC PARAN MAT},
	journal = {BOLETIM DA SOCIEDADE PARANAENSE DE MATEMATICA},
	volume = {31},
	unique-id = {26655691},
	issn = {0037-8712},
	year = {2013},
	eissn = {2175-1188},
	pages = {161-173}
}

@article{MTMT:2339000,
	title = {Balansz számok és általánosításaik},
	url = {https://m2.mtmt.hu/api/publication/2339000},
	author = {Szalay, László},
	journal-iso = {DIMENZIÓK},
	journal = {DIMENZIÓK: MATEMATIKAI KÖZLEMÉNYEK},
	volume = {1},
	unique-id = {2339000},
	issn = {2064-2172},
	year = {2013},
	pages = {11-13}
}

@article{MTMT:1962085,
	title = {Balancing numbers which are products of consecutive integers},
	url = {https://m2.mtmt.hu/api/publication/1962085},
	author = {Tengely, Szabolcs},
	doi = {10.5486/PMD.2013.5654},
	journal-iso = {PUBL MATH DEBRECEN},
	journal = {PUBLICATIONES MATHEMATICAE DEBRECEN},
	volume = {83},
	unique-id = {1962085},
	issn = {0033-3883},
	year = {2013},
	eissn = {2064-2849},
	pages = {197-205}
}

@article{MTMT:22481124,
	title = {t-Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/22481124},
	author = {Dash, KK and Ota, RS and Dash, S},
	journal-iso = {INT J CONTEMP MATH SCI},
	journal = {INTERNATIONAL JOURNAL OF CONTEMPORARY MATHEMATICAL SCIENCES},
	volume = {7},
	unique-id = {22481124},
	issn = {1312-7586},
	year = {2012},
	eissn = {1314-7544},
	pages = {1999-2012}
}

@article{MTMT:23174366,
	title = {Sequence $t$-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/23174366},
	author = {K K, Dash and R S, Ota},
	journal-iso = {INT J CONTEMP MATH SCI},
	journal = {INTERNATIONAL JOURNAL OF CONTEMPORARY MATHEMATICAL SCIENCES},
	volume = {7},
	unique-id = {23174366},
	issn = {1312-7586},
	year = {2012},
	eissn = {1314-7544},
	pages = {2305-2310}
}

@article{MTMT:2341471,
	title = {About the equation $B_m^{(a,b)}=f(x)$},
	url = {https://m2.mtmt.hu/api/publication/2341471},
	author = {Liptai, Kálmán and Olajos, Péter},
	journal-iso = {ANN MATH INFORM},
	journal = {ANNALES MATHEMATICAE ET INFORMATICAE},
	volume = {40},
	unique-id = {2341471},
	issn = {1787-5021},
	year = {2012},
	eissn = {1787-6117},
	pages = {47-55}
}

@article{MTMT:27018826,
	title = {Application of Chybeshev polynomials in factorizations of balancing and Lucas-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/27018826},
	author = {Ray, PK},
	doi = {10.5269/bspm.v30i2.12714},
	journal-iso = {B SOC PARAN MAT},
	journal = {BOLETIM DA SOCIEDADE PARANAENSE DE MATEMATICA},
	volume = {30},
	unique-id = {27018826},
	issn = {0037-8712},
	year = {2012},
	eissn = {2175-1188},
	pages = {49-56}
}

@article{MTMT:26655687,
	title = {Certain Matrices Associated with Balancing and Lucas-balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/26655687},
	author = {Ray, Prasanta Kumar},
	journal-iso = {MATEMATIKA},
	journal = {MATEMATIKA},
	volume = {28},
	unique-id = {26655687},
	issn = {0127-8274},
	year = {2012},
	eissn = {0127-9602},
	pages = {15-22}
}

@article{MTMT:26655697,
	title = {Curious Congruences for Balancing Numbers},
	url = {https://m2.mtmt.hu/api/publication/26655697},
	author = {Ray, Prasanta Kumar},
	journal-iso = {INT J CONTEMP MATH SCI},
	journal = {INTERNATIONAL JOURNAL OF CONTEMPORARY MATHEMATICAL SCIENCES},
	volume = {7},
	unique-id = {26655697},
	issn = {1312-7586},
	year = {2012},
	eissn = {1314-7544},
	pages = {881-889}
}

@article{MTMT:27018825,
	title = {Parallel algorithm for determining the "small solutions" of thue equations},
	url = {https://m2.mtmt.hu/api/publication/27018825},
	author = {Szekrényesi, G},
	journal-iso = {ANN MATH INFORM},
	journal = {ANNALES MATHEMATICAE ET INFORMATICAE},
	volume = {40},
	unique-id = {27018825},
	issn = {1787-5021},
	year = {2012},
	eissn = {1787-6117},
	pages = {125-134}
}

@article{MTMT:23726583,
	title = {Some links of balancing and cobalancing numbers with Pell and associated Pell numbers},
	url = {https://m2.mtmt.hu/api/publication/23726583},
	author = {G K, Panda and Prasanta, Kumar Ray},
	journal-iso = {BULL INST MATH ACAD SIN},
	journal = {BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIAE SINICA},
	volume = {6},
	unique-id = {23726583},
	issn = {0304-9825},
	year = {2011},
	pages = {41-72}
}

@article{MTMT:2775055,
	title = {Multiplying balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/2775055},
	author = {Szakács, Tamás},
	journal-iso = {ACTA UNIV SAPIENTIAE MATH},
	journal = {ACTA UNIVERSITATIS SAPIENTIAE MATHEMATICA},
	volume = {3},
	unique-id = {2775055},
	issn = {1844-6094},
	year = {2011},
	eissn = {2066-7752},
	pages = {90-96}
}

@mastersthesis{MTMT:1989297,
	title = {Combinatorial Diophantine equations},
	url = {https://m2.mtmt.hu/api/publication/1989297},
	author = {Kovács, Tünde},
	publisher = {University of Debrecen},
	unique-id = {1989297},
	year = {2011}
}

@article{MTMT:1427122,
	title = {On generalized balancing sequences},
	url = {https://m2.mtmt.hu/api/publication/1427122},
	author = {Bérczes, Attila and Liptai, Kálmán and Pink, István},
	journal-iso = {FIBONACCI QUART},
	journal = {FIBONACCI QUARTERLY},
	volume = {48},
	unique-id = {1427122},
	issn = {0015-0517},
	year = {2010},
	eissn = {0015-0517},
	pages = {121-128}
}

@article{MTMT:1419242,
	title = {On (a,b)-balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/1419242},
	author = {Kovács, Tünde and Liptai, Kálmán and Olajos, Péter},
	doi = {10.5486/PMD.2010.4857},
	journal-iso = {PUBL MATH DEBRECEN},
	journal = {PUBLICATIONES MATHEMATICAE DEBRECEN},
	volume = {77},
	unique-id = {1419242},
	issn = {0033-3883},
	year = {2010},
	eissn = {2064-2849},
	pages = {485-498}
}

@article{MTMT:1944862,
	title = {Properties of balancing, cobalancing and generalized balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/1944862},
	author = {Olajos, Péter},
	journal-iso = {ANN MATH INFORM},
	journal = {ANNALES MATHEMATICAE ET INFORMATICAE},
	volume = {37},
	unique-id = {1944862},
	issn = {1787-5021},
	year = {2010},
	eissn = {1787-6117},
	pages = {125-138}
}

@mastersthesis{MTMT:23726594,
	title = {Balancing and cobalancing numbers. PhD. Thesis},
	url = {https://m2.mtmt.hu/api/publication/23726594},
	author = {P K, Ray},
	unique-id = {23726594},
	year = {2009}
}

@article{MTMT:23726593,
	title = {Sequence balancing and cobalancing numbers},
	url = {https://m2.mtmt.hu/api/publication/23726593},
	author = {G K, Panda},
	journal-iso = {FIBONACCI QUART},
	journal = {FIBONACCI QUARTERLY},
	volume = {45},
	unique-id = {23726593},
	issn = {0015-0517},
	year = {2007},
	eissn = {0015-0517},
	pages = {265-272}
}

@article{MTMT:1805873,
	title = {On the resolution of simultaneous Pell equations},
	url = {https://m2.mtmt.hu/api/publication/1805873},
	author = {Szalay, László},
	journal-iso = {ANN MATH INFORM},
	journal = {ANNALES MATHEMATICAE ET INFORMATICAE},
	volume = {34},
	unique-id = {1805873},
	issn = {1787-5021},
	year = {2007},
	eissn = {1787-6117},
	pages = {77-87}
}

@article{MTMT:2135332,
	title = {Lucas balancing numbers},
	url = {https://m2.mtmt.hu/api/publication/2135332},
	author = {Liptai, Kálmán},
	journal-iso = {ACTA MATH UNIV OSTRAVIENSIS},
	journal = {ACTA MATHEMATICA UNIVERSITATIS OSTRAVIENSIS},
	volume = {14},
	unique-id = {2135332},
	issn = {1214-8148},
	year = {2006},
	pages = {43-47}
}

@mastersthesis{MTMT:1805908,
	title = {Eredmények a polinomiális és exponenciális diofantikus egyenletek elméletéből},
	url = {https://m2.mtmt.hu/api/publication/1805908},
	author = {Szalay, László},
	unique-id = {1805908},
	year = {2005}
}