Matrix Manipulations for Properties of Pell p-Numbers and their Generalizations

Abstract

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

Keywords

• pell sequence
• pell p-sequence
• matrix
• representation
• 11k31
• 11c20
• 15a15