Generalized Horadam-Leonardo Numbers and Polynomials

In this study, we define and investigate some linear third order polynomials called the generalized Horadam-
Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-
Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sum
formulas for these polynomial sequences. Also, we present some identities and matrices related to these
polynomials. Furthermore, we present some special cases of generalized Horadam-Leonardo polynomials,
namely, generalized Leonardo, generalized John, generalized Ernst, generalized Pisano, generalized Edouard
and generalized Bigollo numbers.