@misc{MTMT:34762407,
	title = {On certain Fibonacci representations},
	url = {https://m2.mtmt.hu/api/publication/34762407},
	author = {Liptai, Kálmán and Németh, L and Szakács, Tamás and Szalay, László},
	unique-id = {34762407},
	year = {2024}
}

@article{MTMT:34742592,
	title = {Decomposable Forms Generated by Linear Recurrences},
	url = {https://m2.mtmt.hu/api/publication/34742592},
	author = {Győry, Kálmán and Pethő, Attila and Szalay, László},
	journal-iso = {J INTEGER SEQ},
	journal = {JOURNAL OF INTEGER SEQUENCES},
	volume = {27},
	unique-id = {34742592},
	abstract = {Consider k ≥ 2 distinct, linearly independent, homogeneous linear recurrences of order k satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree k, and there is a general identity with a suitable exponential expression depending on the recurrences. This identity is a common and very broad generalization of several known identities. Further, if the recurrences are integer sequences, then the diophantine equation associated with the decomposable form and the exponential term has infinitely many integer solutions generated by the terms of the recurrences. We describe a method for the complete factorization of the decomposable form. Both the form and its decomposition are explicitly given if k = 2, and we present a typical example for k = 3. The basic tool we use is the matrix method. © 2024, University of Waterloo. All rights reserved.},
	keywords = {Diophantine equation; Linear recurrence; matrix method; decomposable form; general identity},
	year = {2024},
	eissn = {1530-7638}
}

@article{MTMT:34538292,
	title = {Distribution Generated by a Random Inhomogenous Fibonacci Sequence},
	url = {https://m2.mtmt.hu/api/publication/34538292},
	author = {Liptai, Kálmán and Szalay, László},
	doi = {10.1007/s00009-023-02563-3},
	journal-iso = {MEDITERR J MATH},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {21},
	unique-id = {34538292},
	issn = {1660-5446},
	abstract = {Let G_0=0 G 0 = 0 and G_1=1 G 1 = 1 . The present study deals with the inhomogeneous version \begin{aligned} G_n=G_{n-1}+G_{n-2}+w_{n-2} \end{aligned} G n = G n - 1 + G n - 2 + w n - 2 of the Fibonacci sequence, where w_{n-2} w n - 2 takes value a with probability p , and does value b with 1-p 1 - p . We describe the probability distribution of the values of G_n G n with fixed n , and examine the properties like expected value and variance. The most challenging feature is the fractal-like structure of the distribution.},
	year = {2024},
	eissn = {1660-5454}
}

@article{MTMT:34114194,
	title = {Self-avoiding walks of specified lengths on rectangular grid graphs},
	url = {https://m2.mtmt.hu/api/publication/34114194},
	author = {Major, Laszlo and Németh, László and Pahikkala, Anna and Szalay, László},
	doi = {10.1007/s00010-023-00977-8},
	journal-iso = {AEQUATIONES MATH},
	journal = {AEQUATIONES MATHEMATICAE},
	volume = {98},
	unique-id = {34114194},
	issn = {0001-9054},
	abstract = {The investigation of self-avoiding walks on graphs has an extensive literature. We study the notion of wrong steps of self-avoiding walks on rectangular shape n x m grids of square cells (Manhattan graphs) and examine some general and special cases. We determine the number of self-avoiding walks with one and with two wrong steps in general. We also establish some properties, like unimodality and sum of the rows of the Pascal-like triangles corresponding to the walks. We also present particular recurrence relations on the number of self-avoiding walks on the n x 2 grids with any specified number of wrong steps.},
	keywords = {Unimodality; SELF-AVOIDING WALK; Mathematics, Applied; recurrence sequence; Pascal-like triangle; FINITE LATTICE STRIP},
	year = {2024},
	eissn = {1420-8903},
	pages = {215-239},
	orcid-numbers = {Németh, László/0000-0001-9062-9280}
}

@article{MTMT:34410236,
	title = {Interpolation polynomials associated to linear recurrences},
	url = {https://m2.mtmt.hu/api/publication/34410236},
	author = {Mufid, M.S. and Szalay, László},
	doi = {10.55730/1300-0098.3473},
	journal-iso = {TURK J MATH},
	journal = {TURKISH JOURNAL OF MATHEMATICS},
	volume = {47},
	unique-id = {34410236},
	issn = {1300-0098},
	abstract = {Assume that (Gn)n∈Z is an arbitrary real linear recurrence of order k. In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by (t, Gt) (n0 ≤ t ≤ n1 ). The main result is an explicit formula depends on the explicit formula of Gn and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of (Gn). During the investigations, we developed certain formulae related to the finite differences. © TÜBİTAK},
	keywords = {Linear recurrence; Finite difference; Interpolation polynomial},
	year = {2023},
	eissn = {1303-6149},
	pages = {1932-1943}
}

@{MTMT:34183792,
	title = {Explicit Formulae of Linear Recurrences},
	url = {https://m2.mtmt.hu/api/publication/34183792},
	author = {Szalay, László},
	booktitle = {Mathematics and Computation},
	doi = {10.1007/978-981-99-0447-1_23},
	unique-id = {34183792},
	abstract = {One important and widely studied problem in the theory of linear recurrences is to find explicit formulae for the general term of the sequences. Having an explicit formula facilitates the research of the properties of the sequence we investigate. The main tool is to apply the fundamental theorem of homogeneous linear recurrences, but other approaches may work as well. In the present paper, we concentrate on a specific case when the characteristic polynomial of the sequence has a double zero, and on a general formula.},
	keywords = {Explicit formula; recurrence sequence; Simple zero; Double zero},
	year = {2023},
	pages = {277-284}
}

@{MTMT:34183753,
	title = {Generalizations of the Fibonacci Sequence with Zig-Zag Walks},
	url = {https://m2.mtmt.hu/api/publication/34183753},
	author = {Németh, László and Szalay, László},
	booktitle = {Mathematics and Computation},
	doi = {10.1007/978-981-99-0447-1_26},
	unique-id = {34183753},
	abstract = {The examination of the recurrence sequences associated with combinatorial constructions has been very extensive in the last decades. One of the most famous recurrence sequences is the Fibonacci sequence. We give two digraph constructions defined on the hyperbolic and on the Euclidean square mosaics, respectively, and we introduce two zig-zag type walks associating to the Fibonacci and its generalized sequences. Then we determine the recurrence relations and we give some examples.},
	keywords = {Generalized Fibonacci sequence; recurrence sequence; zig-zag sequence; Hyperbolic Pascal triangle; Zig-zag square graph},
	year = {2023},
	pages = {303-310},
	orcid-numbers = {Németh, László/0000-0001-9062-9280}
}

@article{MTMT:34183473,
	title = {Random inhomogeneous binary recurrences},
	url = {https://m2.mtmt.hu/api/publication/34183473},
	author = {Liptai, Kálmán and Szalay, László},
	journal-iso = {ANN UNIV SCI BP R EÖTVÖS NOM SECT COMPUT},
	journal = {ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA},
	volume = {54},
	unique-id = {34183473},
	issn = {0138-9491},
	year = {2023},
	pages = {253-263}
}

@article{MTMT:34177993,
	title = {A generalization of the hyperbolic Pascal pyramid},
	url = {https://m2.mtmt.hu/api/publication/34177993},
	author = {Belbachir, Hacène and Rami, Fella and Németh, László and Szalay, László},
	doi = {10.1007/s13226-023-00481-4},
	journal-iso = {INDIAN J PURE AP MAT},
	journal = {INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS},
	unique-id = {34177993},
	issn = {0019-5588},
	year = {2023},
	eissn = {0975-7465},
	orcid-numbers = {Rami, Fella/0000-0002-1701-6151; Németh, László/0000-0001-9062-9280}
}

@article{MTMT:34131814,
	title = {TRIANGULAR DIOPHANTINE TUPLES FROM {1, 2}},
	url = {https://m2.mtmt.hu/api/publication/34131814},
	author = {Filipin, A. and Szalay, László},
	doi = {10.21857/ygjwrcp48y},
	journal-iso = {RAD HRVAT AKAD ZNAN UMJET MAT ZNAN},
	journal = {RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI},
	volume = {27},
	unique-id = {34131814},
	issn = {1845-4100},
	abstract = {In this paper, we prove that there does not exist a set of four positive integers {1, 2, c, d} such that a product of any two of them increased by 1 is a triangular number. © 2023, Croatian Academy of Sciences and Arts. All rights reserved.},
	keywords = {linear forms in logarithms; Diophantine m-tuples; Pell equations},
	year = {2023},
	eissn = {1849-2215},
	pages = {55-70}
}