Results 41 to 50 of about 1,467 (207)

Generalized Hybrid Fibonacci and Lucas p-numbers

, 2022
The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers.
Kocer, E. Gokcen, Alsan, Huriye
core   +1 more source

Fibonacci and Lucas Numbers [PDF]

, 2017
U ovom diplomskom radu dan je uvod u Fibonaccijeve i Lucasove brojeve. U prvom dijelu rada definirali smo Fibonaccijeve i Lucasove brojeve, dokazali različite identitete koji vrijede za Fibonaccijeve brojeve, neke koji vrijede za Lucasove brojeve i neke ...
Zirdum, Ivona
core   +2 more sources

k-Fibonacci and k-Lucas Differential Equations with New Spirals [PDF]

Mathematics Interdisciplinary Research
‎Fibonacci sequences and the spirals formed by employing them have found vast applications in creations and natural phenomena‎. ‎In this study‎, ‎new k-Fibonacci and k-Lucas differential equations are proposed‎.
Mehmet Pakdemirli, İhsan Dolapci
doaj   +1 more source

Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers

Mathematics, 2022
Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
doaj   +1 more source

-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, Asci, Mustafa, Aydinyuz, Suleyman, Mustafa Asci   +3 more
core   +1 more source

A new approach to Fibonacci Tessarines with Fibonacci and Lucas number components

Adıyaman University Journal of Science, 2021
In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas numbers we define Fibonacci tessarines and Lucas tessarines. We obtain Binet formulae, D’ocagnes identity and Cassini identity for these tessarines. We also give the identities of Fibonacci negatessarines and Lucas negatessarines and define new vector which are ...
BABADAĞ, Faik, USLU, Merve
openaire   +2 more sources

A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Journal of Mathematics, 2023
We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
doaj   +1 more source

Reciprocal Formulae among Pell and Lucas Polynomials

Mathematics, 2022
Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions.
Mei Bai, Wenchang Chu, Dongwei Guo
doaj   +1 more source

Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions [PDF]

Notes on Number Theory and Discrete Mathematics
The aim of this paper is to establish some novel identities for hyperbolic k-Fibonacci octonions and k-Lucas octonions. We prove these properties using the identities of k-Fibonacci and k-Lucas numbers, which we determined previously.
A. D. Godase
doaj   +1 more source

Hybrinomials Related to Hyper-Fibonacci and Hyper-Lucas Numbers [PDF]

, 2023
ybrid number system is a generalization of complex, hyperbolic and dual numbers. Hybrid numbers and hybrid polynomials have been the subject of much research in recent years.
Mersin, Efruz Özlem
core   +1 more source