Generating functions of binary products of (p,q)-Fibonacci-like numbers with odd and even certain numbers and polynomials

Abstract

In this paper, we study the symmetric and the generating functions for odd and even terms of the second-order linear recurrence sequences. we introduce a operator in order to derive a new family of generating functions of odd and even terms of Mersenne numbers, Mersenne Lucas numbers, (p,q)- Fibonacci-like numbers, k-Pell polynomials and k-Pell Lucas polynomials. By making use of the operator defined in this paper, we give some new generating functions of the products of (p,q)-Fibonacci-like numbers with odd and even terms of certain numbers and polynomials.