The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence

Abstract

I n this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal p-sequence. The generating matrix, the generalized Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are investigated. Moreover, certain sum formula consisting of the terms of the generalized Jacobsthal p-sequence are given