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Fibonacci numbers and orthogonal polynomials
Arab Journal of Mathematical Sciences, 2011 A note dated June 2007 has been added with some historical comments.
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An identity for the Fibonacci and Lucas numbers [PDF]
Glasgow Mathematical Journal, 1993 In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following ...
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Total Graph Interpretation of the Numbers of the Fibonacci Type
Journal of Applied Mathematics, 2015 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give
Urszula Bednarz +2 more
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On Diophantine quadruples of Fibonacci numbers
Glasnik Matematicki, 2017 We show that there are only finitely many Diophantine quadruples, that is, sets of four positive integers {a1,a2,a3,a4} such that aiaj+1 is a square for all 1 ≤ i < j ≤ 4, consisting of Fibonacci numbers.
Fujita, Yasutsugu, Luca, Florian
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On Doubled and Quadrupled Fibonacci Type Sequences
Annales Mathematicae SilesianaeIn this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled ...
Yilmaz Nur Şeyma +3 more
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Psychoacoustic Properties of Fibonacci Sequences
Acta Polytechnica, 2008 1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones.
J. Sokoll, S. Fingerhuth
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On the Frobenius Number of Fibonacci Numerical Semigroups [PDF]
, 2007 J. M. MARIN +2 more
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Pseudo-random number generator based on linear congruence and delayed Fibonacci method
, 2021 Radosław Cybulski
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Applicable Analysis and Discrete Mathematics, 2009 The scope of the paper is the definition and discussion of the polynomial generalizations of the Fibonacci numbers called here ?-Fibonacci numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between ?-Fibonacci numbers and Fibonacci and Lucas numbers are proven in this paper.
Roman Wituła, Damian Słota
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On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
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