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2 results on '"Fibonacci octonion"'

1. Some unrestricted Fibonacci and Lucas hyper-complex numbers.

Author

BILGICI, GÖKSAL and DAŞDEMIR, AHMET

Subjects
*LUCAS numbers, *COMPLEX numbers, *IDENTITY (Psychology), *GENERATING functions, *CAYLEY numbers (Algebra), *FIBONACCI sequence, *QUATERNIONS
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. [ABSTRACT FROM AUTHOR]

Published
2020
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2. On fibonacci and lucas generalized octonions

Author

Goksal Bilgici, Ünal, Z., Togeşer, U., Mert, T., [Bilgici, Goksal] Kastamonu Univ, Educ Fac, Dept Comp Educ & Instruct Technol, Kastamonu, Turkey -- [Unal, Zafer -- Tokeser, Umit] Kastamonu Univ, Fac Arts & Sci, Dept Math, Kastamonu, Turkey -- [Mert, Tugba] Cumhuriyet Univ, Fac Arts & Sci, Dept Math, Sivas, Turkey, and UNAL, ZAFER -- 0000-0003-2445-1028

Subjects
Fibonacci octonion, Lucas octonion, Generalized octonion
Abstract

WOS: 000430156300004, We study on Fibonacci and Lucas generalized octonions over the algebra O(a, b, c) where a, b and c are real numbers. We obtain Binet formulas for the Fibonacci and Lucas generalized octonions. Also, we give many identities for these octonions including Catalan's identity, Cassini's identity and d'Ocagne's identity.

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