The first study of the Jacobsthal-Mulatu Numbers

The aim of this study is to find a sequence of Jacobsthal-type numbers, which we will denote by {JMn}n≥0 and name as the sequence of Jacobsthal-Mulatu, such that each term of the Jacobsthal-Lucas sequence, denoted by {jn}n≥0, is an average term between JMn and Jn, where {Jn}n≥0 is the classical Jacobsthal sequence. We investigated some key characteristics of the sequence of Jacobsthal-Mulatu. In this study, we present some interesting properties of these sequences of numbers explored in connection with the sequences {Jn}n≥0 and {jn}n≥0.