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


Nabiha Saba, Ali Boussayoud




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.