Sums of the Squares of Terms of Sequence {u(n)}

Abstract

In this paper, we consider generalized Fibonacci type second order linear recurrence {u(n)}. We derive a generating matrix for both the sums of squares, Sigma(n)(i=0) u(i)(2) and the products of the form u(n)u(n+2). We also derive explicit formulas for the sums and products by using matrix methods. Then we give a matrix method to generate the sums of product of two consecutive terms u(n)u(n+1) as well as the product, u(n)u(n+2). Further we give generating functions and combinatorial representations of the sums of squares of terms of {u(n)} and the product, u(n)u(n+2).