Sums and Products of the Jacobsthal and Jacobsthal-Lucas Numbers and Their Determinantal Representation

Abstract

We investigate the Jacobsthal numbers \(\{J_n\}\) and Jacobsthal-Lucas numbers \(\{j_n\}\). Let \(\mathcal{J}_n = J_n \times j_n\) and \(\mathcal{J}_n = J_n + j_n\).In this paper, we give some determinantal and permanental representations for \(\mathcal{J}_n\) and \(\mathcal{J}_n\). Also, complex factorization formulas for the numbers are presented.