On k-Fibonacci hybrid numbers and their matrix representations

Abstract

In this paper, k-Fibonacci hybrid numbers are defined. Also, some algebraic properties of k-Fibonacci hybrid numbers such as Honsberger identity, Binet Formula, generating functions, d'Ocagne identity, Cassini and Catalan identities are investigated. In addition, we also give 2x2 and 4 x 4 representations of the k-Fibonacci hybrid numbers HFk,n.