Results 31 to 40 of about 1,051 (219)

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
doaj   +1 more source

A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers

Journal of Mathematics, 2021
We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers.
Jiangming Ma, Tao Qiu, Chengyuan He
doaj   +1 more source

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

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

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

Annales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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 fast recurrence for Fibonacci and Lucas numbers

CoRR, 2021
We derive the double recurrence $e_n = \frac{1}{2}(a_{n-1}+5b_{n-1}); f_{n} = \frac{1}{2}(a_{n-1}+b_{n-1})$ with $e_0=2;f_0=0$ for the Fibonacci numbers, leading to an extremely simple and fast implementation. Though the recurrence is probably not new, we have not been able to find a reference for it.
openaire   +2 more sources

New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
doaj   +1 more source

On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

, 2022
We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers.
Özkan, Engin, Kuloğlu, Bahar
core   +1 more source

ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]

Journal of the Korean Mathematical Society, 2005
The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
openaire   +4 more sources