Some unrestricted Fibonacci and Lucas hyper-complex numbers - Bilgici, Göksal; Daşdemir, Ahmet (University of Tartu, 2020)
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.
Keywords: Fibonacci and Lucas numbers and polynomials and generalizations; Fibonacci octonion; Fibonacci sedenion; Fibonacci quaternion