Horadam Octonions

TL;DR

This paper introduces Horadam octonions, a new mathematical construct based on the Horadam sequence, and explores their fundamental properties, formulas, and identities.

Contribution

It defines Horadam octonions and derives their key properties, including Binet-like formula, generating function, and Cassini identity, expanding the understanding of octonion sequences.

Findings

Derived Binet-like formula for Horadam octonions

Established generating function for Horadam octonions

Proved Cassini identity for Horadam octonions

Abstract

In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence. Then, we obtain their Binet-like formula, ordinary generating function and Cassini identity.