On the Connections between Padovan Numbers and Fibonacci p-Numbers

Abstract

In this paper, we define the Fibonacci-Padovan p-sequence and then we discuss the connection of the Fibonacci-Padovan p-sequence with the Padovan sequence and Fibonacci p-sequence. In addition, we obtain miscellaneous properties of the Fibonacci-Padovan p-numbers such as the Binet formulas, the exponential, combinatorial, permanental and determinantal representations, and the sums of
certain matrices.

Key words and phrases. Padovan sequence, Fibonacci p-sequence, matrix representation.

2010 Mathematics Subject Classification. 11K31; 11C20; 15A15