In this paper, we present a generalization of well-known k-Fibonacci sequence. Namely, defined generalized This sequence generalizes others, sequence, classical Fibonacci Pell and Jacobsthal We establish some the interesting properties Also, obtain generating function for them.

The main purpose of this paper is to define a new regular matrix by using Fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

Let us begin by defining a generalized Fibonacci sequence (gn) with all gn in some abelian group as a sequence that satisfies the recurrence gn = gn−1 + gn−2 as n ranges over Z. The Fibonacci sequence (Fn) is the generalized Fibonacci sequence with integer values defined by F0 = 0 and F1 = 1. Recall also the Binet formula: for any integer n, Fn = (α − β)/ √ 5, where α = (1 + √ 5)/2 and β = (1− ...

The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths and cycles, respectively. In the first part of the work we provide a formula for the number of edges of the Hasse diagram of the independent sets of the h power of a path ordered by inclusion. For h = 1 such a diagram is called a Fibonacci cube, and for h > 1 we obtain a generalization of th...

the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

In this paper, we suggest a lower and an upper bound for the Generalized Fibonaccip-Sequence, for different values of p. The Fibonacci-p-Sequence is a generalization of the Classical Fibonacci Sequence. We first show that the ratio of two consecutive terms in generalized Fibonacci sequence converges to a p-degree polynomial and then use this result to prove the bounds for generalized Fibonacci-...

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formu...

The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from elementary properties of the Fibonacci numbers. 1 Preliminaries The well-known sequence of Fibonacci numbers (sequence A000045 in the On-Line Encyclopedia of Int...