On Horadam finite operator hybrid numbers

Abstract

In this paper, we introduce and study a new hybrid number sequence with Horadam numbers and a finite operator, called Horadam finite operator hybrid numbers. We derive recurrence relation, Binet-like formula, ordinary generating function, exponential generating function, Poisson generating function, and summation formula for Horadam finite operator hybrid numbers. Moreover, we give matrix representation and Cassini's identities for these numbers.