Results 101 to 110 of about 903 (200)

On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]

Mathematica Bohemica
For an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah, Salah Eddine Rihane, Alain Togbé   +2 more
doaj   +1 more source

Q-Analogues of biperiodic fibonacci and lucas sedenions [PDF]

, 2021
Quantum calculus has an important areas in many areas such as number theory, physics and mathematics. In this paper, by taking some useful notations from quantum calculus, we define the biperiodic Fibonacci and Lucas sedenions based on a q-parameter ...
Köme, Sure, Gün, Hafize
core  

Determinant Representations of Sequences: A Survey

Special Matrices, 2014
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices.
Moghaddamfar A. R., Salehy S. Navid, Salehy S. Nima   +2 more
doaj   +1 more source

An algorithm for complex factorization of the bi-periodic Fibonacci and Lucas polynomials [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we consider the factorization of generalized sequences, by employing a method based on trigonometric identities. The new method is of reduced complexity and represents an improvement compared to existing results.
Baijuan Shi, Can Kızılateş
doaj   +1 more source

Some new properties of k Fibonacci sequences

, 2015
Some new properties of k Fibonacci sequences and k Lucas sequences are represented.
Ashok Godase (820536)
core   +1 more source

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  

Visualization of Metallic Sequences and its Extensions: A Combinatorial approach Via Board and Tiles

REDIMAT
The 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, Maria Graciene Moreira Dos Santos, Paula Maria Machado Cruz Catarino   +2 more
doaj   +1 more source

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

Verbena officinalis Verbenaceae (Lamiales): a new plant model system for phyllotaxis research. [PDF]

J Plant Res, 2021
Zagórska-Marek B, Turzańska M, Chmiel K.   +2 more
europepmc   +1 more source

On the sums of Fibonacci and Lucas sequences or the art of cancelling $1−x$

Elemente der Mathematik, 2017
The author establishes the identity \[ \sum_{k=0}^n m^kL-k + (m-2) \sum_{k=0}^{n+1} m^{k-1} F_k = m^{n+1} F_{n+1}, \] for nonnegatiev integer \(n\) and real \(m>0\), \(F_n\), \(L_n\) denote the Fibonacci numbers and Lucas numbers, thereby generalizing previous Fibonacci-Lucas relations of Sury and Marques.
openaire   +1 more source