General Approach in Computing Sums of Products of Binary Sequences

Abstract

In this paper we find a general approach to find closed forms of sums of products of arbitrary sequences satisfying the same recurrence with different initial conditions. We apply successfully our technique to sums of products of such sequences with indices in (arbitrary) arith- metic progressions. It generalizes many results from literature. We propose also an extension where the sequences satisfy different recur- rences.