Generalized Horadam-Leonardo Numbers and Polynomials
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, Zonguldak-67100, Turkey.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Horadam polynomials, fibonacci polynomials, tribonacci polynomials, horadam-leonardo polynomials, third order recurrence relations