On horadam octonions

Abstract

In this paper, we introduce the Horadam octonions, we give the Binet formula, generating function and exponential generating function of these octonions. Also, we obtain some identities for Horadam octonions including Catalan, Cassini and d'Ocagne identities. By using these results, we have the Binet formula, generating function, summation formula, Catalan and d'Ocagne identities for Fibonacci, Lucas, Jacobsthal, Jacobsthal-Lucas, Pell and Pell-Lucas octonions. Finally, we introduce the matrix generator for Horadam octonions and this generator gives the Cassini formula for the Horadam octonions. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.