Matrix manipulations for properties of Fibonacci p-numbers and their generalizations

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