Binomial sums with k-Jacobsthal and k-Jacobsthal–Lucas numbers

Abstract

In this paper, we derive some important identities involving k-Jacobsthal and k-Jacobsthal–Lucas numbers. Moreover, we use multinomial theorem to obtain distinct binomial sums of k-Jacobsthal and k-Jacobsthal–Lucas numbers.

On the recurrences of the Jacobsthal sequence

“…Proof. The relationship of the Jacobsthal arrays with the Jacobsthal number is obtained by using (11) and (12). □ Theorem 2.2.…”

Mersenne Lucas numbers and complete homogeneous symmetric functions

“…In addition, Tasci defined and studied Gaussian Mersenne numbers in [4]. Moreover, studies on the different Gaussian polynomials sequences like Gaussian Jacobsthal, Gaussian Jacobsthal Lucas, Gaussian Pell and Gaussian Pell Lucas polynomials can be found in the papers [6], [13], [14]. Definition 1.…”