On generalizations of the Jacobsthal sequence

Abstract

In this paper, the generalized Jacobsthal and generalized complex Jacobsthal and generalized dual Jacobsthal sequences using the Jacobsthal numbers are investigated. Also, special cases of these sequences are investigated. Furthermore, recurrence relations, vectors, the golden ratio and Binet's formula for the generalized Jacobsthal sequences and generalized dual Jacobsthal sequences are given.