On Binomial Sums for the General Second Order Linear Recurrence

Abstract

In this short paper we establish identities involving sums of products of binomial coefficients and coefficients that satisfy the general second-order linear recurrence. We obtain generalizations of identities of Carlitz, Prodinger and Haukkanen.

On some Horadam symbol elements

“…Kilic [16] studied some binomial sums involving the (p, q)−Fibonacci numbers. The following theorem provides a similar sum formula for the Horadam symbol elements.…”

A short remark on Horadam identities with binomial coefficients

“…More recently, some authors also worked on generalizations and derived expressions for sums with weighted binomial sums, sums with polynomials and sums where only half of the binomial coefficients are used. We refer to [2] and [10][11][12][13][14]. Adegoke [1] generalized many of the above results and derived summation identities involving Horadam numbers and binomial coefficients, some of which we will encounter below.…”

The Relation Between Chebyshev Polynomials and Jacobsthal and Jacobsthal Lucas Sequences

“…Horzum and Koçer studied the properties of Horadam polynomial sequences in [8]. The authors established identities involving sums of products of binomial coefficients that satisfy the general second order linear recurrence in [9]. In [10], the authors obtained Horadam numbers with positive and negative indices by using determinants of some special tridiagonal matrices.…”