On The Connections Between Jacobsthal Numbers and Fibonacci p-Numbers

Abstract

In this paper, we define the Fibonacci-Jacobsthal p-sequence and then we discuss the connection of the Fibonacci-Jacobsthal p-sequence with Jacobsthal and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of Fibonacci-Jacobsthal p-numbers by the aid of the nth power of the generating matrix the Fibonacci-Jacobsthal p-sequence. Furthermore, we derive relationships between the Fibonacci-Jacobsthal p-numbers and their permanent, determinant and sums of certain matrices.