Double binomial sums and double sums related with certain linear recurrences of various order

Abstract

In this paper, we derive new double binomial sums families related with generalized second, third and certain higher order linear recurrences. We also present various parametric generalizations of some results of [1, 2]. Finally we present some interesting double sums including only one binomial coefficient related with certain number sequences of various order. We use generating function methods to prove claimed results.