A Note on Hyper-Dual Numbers with the Leonardo-Alwyn Sequence

Abstract

We are interested in identifying hyper-dual numbers with the Leonardo-Alwyn sequence components. We investigate their homogeneous and non-homogeneous recurrence relations, the Binet’s formula, and the generating function. With these algebraic properties, we are able to obtain some special cases of hyper-dual numbers with the Leonardo-Alwyn sequence according to $p,q$ and $c$ (multipliers).