On characteristic polynomial of higher order generalized Jacobsthal numbers

Abstract

Abstract In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c) $(k,c)$-Jacobsthal sequence (Jn(k,c)) $(J^{(k,c)}_{n})$ for any integers n, k≥2 $k\geq 2$ and a real number c>0 $c>0$. 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 Eneström–Kakeya theorem.

Keywords

• Linear recurrence sequence
• Jacobsthal sequence
• Generalized Jacobsthal sequence
• Computation
• Polynomial
• Matrix theory