Results 11 to 20 of about 1,036 (80)
On the greatest common divisor of $n$ and the $n$th Fibonacci number [PDF]
, 2017 Let $\mathcal{A}$ be the set of all integers of the form $\gcd(n, F_n)$, where $n$ is a positive integer and $F_n$ denotes the $n$th Fibonacci number.
Leonetti, Paolo, Sanna, Carlo
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A Family of the Zeckendorf Theorem Related Identities [PDF]
, 2015 In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation.
Martinjak, Ivica
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Extended Fibonacci numbers and polynomials with probability applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 50, Page 2681-2693, 2004., 2004 The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained.
Demetrios L. Antzoulakos
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International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2507-2518, 2003., 2003 We prove that powers of 4‐netted matrices (the entries satisfy a four‐term recurrence δai,j = αai−1,j + βai−1,j + γai,j−1) preserve the property of nettedness: the entries of the eth power satisfy δeai,j(e)=αeai−1,j(e)+βeai−11,j−(e)+γeai,j−1(e), where the coefficients are all instances of the same sequence xe+1 = (β + δ)xe − (βδ + αγ)xe−1.
Pantelimon Stănică
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A Study on Fibonacci and Lucas Bihypernomials
Discussiones Mathematicae - General Algebra and Applications, 2022 The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the ...
Szynal-Liana Anetta, Włoch Iwona
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A note on Fibonacci matrices of even degree
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 8, Page 457-469, 2001., 2001 This paper presents a construction of m‐by‐m irreducible Fibonacci matrices for any even m. The proposed technique relies on matrix representations of algebraic number fields which are an extension of the golden section field. The explicit construction of some 6‐by‐6 and 8‐by‐8 irreducible Fibonacci matrices is given.
Michele Elia
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Annales Mathematicae Silesianae, 2020 Let {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e.
Farhadian Reza, Jakimczuk Rafael
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Fibonacci and Lucas Polynomials in n-gon
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices.
Kuloğlu Bahar +2 more
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A curious property of series involving terms of generalized sequences
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 1, Page 55-63, 2000., 2000 Here we are concerned with series involving generalized Fibonacci numbers Un (p, q) and generalized Lucas numbers Vn (p, q). The aim of this paper is to find triples (p, q, r) for which the series Un (p, q)/rn and Vn (p, q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n.
Odoardo Brugia, Piero Filipponi
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The Generalization of Gaussians and Leonardo’s Octonions
Annales Mathematicae Silesianae, 2023 In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented.
Vieira Renata Passos Machado +3 more
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