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 sumformulas for these polynomial sequences. Also, we present some identities and matrices related to thesepolynomials. Furthermore, we present some special cases of generalized Horadam-Leonardo polynomials,namely, generalized Leonardo, generalized John, generalized Ernst, generalized Pisano, generalized Edouardand generalized Bigollo numbers.