Some unrestricted fibonacci and lucas hyper-complex numbers

Abstract

A number of studies have investigated the Fibonacci quater-nions and octonions that include consecutive terms of the Fibonacci sequence. This paper presents a new generalization of Fibonacci quater-nions, octonions and sedenions, where non-consecutive Fibonacci numbers are used. We present the Binet formulas, generating functions and some identities for these new types of hyper-complex numbers.