Some Properties of Dual Fibonacci and Dual Lucas Octonions

Abstract

Halici (Adv Appl Clifford Algebr 25(4):905–914, 2015) defined dual Fibonacci and dual Lucas octonions by the relations Q~ n= Qn+ εQn+1 and P~ n= Pn+ εPn+1 for every integer n where Qn and Pn are the Fibonacci and Lucas octonions respectively, and ε is the dual unit. The aim of this paper is to investigate properties of dual Fibonacci and dual Lucas octonions. After obtaining the Binet formulas for the sequences {Q~n}n=0∞ and {P~n}n=0∞, we derive some identities for these sequences such as Catalan’s, Cassini’s and d’Ocagne’s identities.