Some unrestricted Fibonacci and Lucas hyper-complex numbers

Keywords: Fibonacci quaternion, Fibonacci octonion, Fibonacci sedenion

Abstract

A number of studies have investigated the Fibonacci quaternions and octonions that include consecutive terms of the Fibonacci sequence. This paper presents a new generalization of Fibonacci quaternions, 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.

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Published
2020-09-23
Section
Articles