Results 101 to 110 of about 613 (205)
-order Fibonacci and Lucas hybrid numbers
, 2021 In this study, we describe the generalized k-order Fibonacci and Lucas numbers and give some important results with specific choices. The main purpose of this study is to define the generalized k-order Fibonacci hybrid and Lucas hybrid numbers and give ...
Suleyman Aydinyuz +3 more
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Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences
Advances in Difference Equations, 2020 In this paper, we consider a generalization of Horadam sequence {wn} $\{ w_{n} \} $ which is defined by the recurrence relation wn=χ(n)wn−1+cwn−2 $w_{n}=\chi ( n ) w_{n-1}+cw_{n-2}$, where χ(n)=a $\chi ( n ) =a$ if n is even, χ(n)=b $\chi ( n ) =b$ if n ...
Elif Tan, Ho-Hon Leung
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The p-adic valuation of Lucas sequences
, 2016 Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2 − aX − b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms ...
Sanna, Carlo
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A trick around Fibonacci, Lucas and Chebyshev
, 2014 23 pagesInternational audienceIn this article, we present a trick around Fibonacci numbers which can be found in several magic books. It consists in computing quickly the sum of the successive terms of a Fibonacci-like sequence.
Lachal, Aimé
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Bi-periodic Fibonacci and Lucas matrix sequences
, 2019 Son yıllarda, bilim dünyasının ilgisini çeken ve birçok alanda karşımıza çıkan Fibonacci, Lucas, Pell, Pell-Lucas, -Fibonacci ve -Lucas sayı dizileri ile ilgili pek çok çalışma vardır.
Coşkun, Arzu
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Unique Properties of the Fibonacci and Lucas Sequences
, 2017 The algebraic structure of the set of all Fibonacci-like sequences, which includes the Fibonacci and Lucas sequences, is developed, utilizing an isomorphism between this set and a subset of the 2 by 2 integer matrices.
Parry, Stephen
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Primes in Fibonacci n-step and Lucas n-step Sequences
, 2005 We search for primes in the Fibonacci n-step and Lucas n-step sequences, which are the natural generalizations of the Fibonacci and Lucas numbers. While the Fibonacci n-step sequences are nearly devoid of primes, the Lucas n-step sequences are prime-rich.
Tony D. Noe, Jonathan Vos Post
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Visualization of Metallic Sequences and its Extensions: A Combinatorial approach Via Board and Tiles
REDIMATThe study of recurring numerical sequences interests numerous researchers in several countries. We observe that, with a historical legacy from the Fibonacci and Lucas sequences, numerous ways of approaching and generalizing these and other sequences ...
Francisco Regis Vieira Alves +2 more
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Fibonacci and Lucas sequences at negative indices
, 2016 This study investigate the Fibonacci and Lucas sequences at neg- ative indices. In this paper we give the formulas of F????(nk+r) and L????(nk+r) depending on whether the indices are odd or even.
Akyüz, Zeynep, Halıcı, Serpil
core
The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach. [PDF]
Heliyon, 2022 Anđelić M, da Fonseca CM, Yılmaz F.
europepmc +1 more source