Results 21 to 30 of about 616 (205)
A note on the bi-periodic Fibonacci and Lucas matrix sequences [PDF]
Applied Mathematics and Computation, 2018 Abstract In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix sequences. We express that some behaviors of bi-periodic Lucas numbers also can be obtained by
Arzu Coşkun
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The degree sequence of Fibonacci and Lucas cubes
Discrete Mathematics, 2011 The Fibonacci cube $\Gamma_n$ is the subgraph of the $n$-cube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $\Lambda_n$ is obtained from $\Gamma_n$ by removing vertices that start and end with 1. It is proved that the number of vertices of degree $k$ in $\Gamma_n$ and $\Lambda_n$ is $\sum_{i = 0}^k \binom{n-2i}{k-i} \
Sandi Klavžar +2 more
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Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences
Mathematics, 2020 In this paper we consider a generalized bi-periodic Fibonacci {fn} and a generalized bi-periodic Lucas sequence {qn} which are respectively defined by f0=0, f1=1, fn=afn−1+cfn−2 (n is even) or fn=bfn−1+cfn−2 (n is odd), and q0=2d, q1=ad, qn=bqn−1+cqn−2 ...
Younseok Choo
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Fibonacci and k Lucas Sequences as Series of Fractions [PDF]
Mathematical Journal of Interdisciplinary Sciences, 2016 In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature.
A. D. Godase, M. B. Dhakne
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Generalizations of Fibonacci and Lucas sequences [PDF]
, 2002 The author studies the Hecke group \(H(\sqrt q)\) (\(q\) a prime \(\geq 5\)), the subgroup of \(\text{PSL}(2, \mathbb{Z})\) generated by \(z \to {- {1/z}}\) and \(z \to {z + \sqrt q}\). This group can also be generated by \(z \to {- {1/z}}\) and an element \(S\) whose matrix representation is \[ \left(\begin{matrix} 0 & {-1} \\ 1 & {\sqrt q} \end ...
Yilmaz Özgür, Nihal
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Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences [PDF]
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 The uniqueness of the sum of the elements of finite subsets of the odd oreven indexed Fibonacci and Lucas sequences are proved. Moreover, it is shownthat the odd or even indexed Fibonacci and Lucas sequences are superincreasingsequences.
Alparslan Kargın +2 more
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On waiting time distribution of runs in a Fibonacci and Lucas sequences [PDF]
European Journal of Science and Technology, 2021 Doğal fenomenlerin kesin bir manada tanımlanması, öngörülmesi ve anlaşılmasıyla ilgili yeni matematiksel aygıtlar geliştirme ihtiyacı giderek artmaktadır. Bu çalışmanın amacı, Fibonacci ve Lucas dizilerinin matematiksel çerçevesini modern matematiksel formüller ile desteklemek amacıyla genişletmektir.
EDABAA, Abd Anasır, BİLGİCİ, Göksal
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Fibonacci Cartan and Lucas Cartan numbers [PDF]
Open MathematicsThis study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers.
Öztürk İskender, Çakır Hasan
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Fibonacci and Lucas Sequences in Aperiodic Monotile Supertiles [PDF]
CoRR10 pages, 21 ...
Dong, Shiying
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Generalized Fibonacci-Lucas Sequence [PDF]
Turkish Journal of Analysis and Number Theory, 2014 The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field.
Bijendra Singh +2 more
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