Properties of Generalized k-Jacobsthal like Sequence Using Matrices.

The Jacobsthal sequence has been generalized in many ways, some by preserving the initial conditions, others by preserving the recurrence relation. In this paper, we define a new generalization {Mk,n}∞ n = 1,with initial conditions Mk,o = 2Mk,1= m+k, which is generated by the recurrence relation Mk,n+1 = kMk,n + 2Mk,n-1 for n = 1, where k, m are integer numbers. Some new properties concerning this new generalization have been described using matrix algebra. [ABSTRACT FROM AUTHOR]