Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions

Abstract

In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.

Keywords

• k-fibonacci numbers
• k-lucas numbers
• quaternions
• generating function