On characteristic polynomial of higher order generalized Jacobsthal numbers

Abstract

In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c)}-Jacobsthal sequence (Jn(k,c)) for any integers n, k >= 2. In particular, we find information about roots of its characteristic polynomial. For that purpose, we combine some powerful tools such as Marden's method, the Perron-Frobenius theorem, and the Enestrom-Kakeya theorem.