Results 21 to 30 of about 613 (205)

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
exaly   +3 more sources

Fibonacci and k Lucas Sequences as Series of Fractions

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
openaire   +3 more sources

Generalizations of Fibonacci and Lucas sequences

, 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
openaire   +7 more sources

Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences

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, Emre Kişi, Halim Özdemir   +2 more
doaj   +1 more source

On waiting time distribution of runs in a Fibonacci and Lucas sequences

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
openaire   +4 more sources

Fibonacci Cartan and Lucas Cartan numbers

Open Mathematics
This 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
doaj   +2 more sources

Fibonacci and Lucas Sequences in Aperiodic Monotile Supertiles

CoRR
10 pages, 21 ...
Dong, Shiying
openaire   +3 more sources

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, Omprakash Sikhwal, Yogesh Kumar Gupta   +2 more
openaire   +3 more sources

On the k-Fibonacci and k-Lucas spinors [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne's identity, Vajda's identity ...
Munesh Kumari, Kalika Prasad, Robert Frontczak   +2 more
doaj   +1 more source

Pseudoprimality related to the generalized Lucas sequences [PDF]

, 2021
Some arithmetic properties and new pseudoprimality results concerning generalized Lucas sequences are presented. The findings are connected to the classical Fibonacci, Lucas, Pell, and Pell–Lucas pseudoprimality.
Andrica, Dorin, Bagdasar, Ovidiu
core   +1 more source