Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse of two kinds generalized k-Fibonacci matrices. We derive some identities the sequence. investigate Cholesky factorization symmetric matrix by using these identities.

Abstract Following Bridgeman, we demonstrate several families of infinite dilogarithm identities associated with Fibonacci numbers, Lucas convergents continued fractions even periods, and terms arising from various recurrence relations.

This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation , 2 , 1 , 0 , 3 , 2 3 , 2 , , = ≥ + = − − m n w w w n m n m m n m , with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the...

Numerous writers appear to have been fascinated by the many interesting summation identitites involving the Fibonacci and related Lucas numbers. Various types of formulas are discussed and various methods are used. Some involve binomial coefficients [2 ] , [4 ] . Generating function methods are used in [2] and [5] and higher powers appear in [6] . Combinations of these or other approaches appea...

We prove some finite sum identities involving reciprocals of the binomial and central coefficients, as well harmonic, Fibonacci Lucas numbers, which recover previously known results, while others are new.

We study the previously introduced bracketed tiling construction and obtain direct proofs of some identities for the Fibonacci and Lucas numbers. By adding a new type of tile we call a superdomino to this construction, we obtain combinatorial proofs of some formulas for the Fibonacci and Lucas polynomials, which we were unable to find in the literature. Special cases of these formulas occur in ...

In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini d’Ocagne’s identities. Also, calculate summation formulas for involving Fibonacci Lucas numbers.

The bi-periodic Fibonacci sequence also known as the generalized Fibonacci sequence was fırst introduced into literature in 2009 by Edson and Yayenie [9] after which the bi-periodic Lucas sequence was defined in a similar fashion in 2004 by Bilgici [5]. In this study, we introduce a new generalization of the Jacobsthal numbers which we shall call bi-periodic Jacobsthal sequences similar to the ...

Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the inverse of LOG. In particular, LOG takes a convolution product of generalized Fibonacci polynomials to a sum of generalized Lucas polynomials and EXP takes the sum to the convolution product. We use this structure to ...