Sums of the squares of terms of sequence {u n }

Abstract

In this paper, we consider generalized Fibonacci type second order linear recurrence {un}. We derive a generating matrix for both the sums of squares, ∑i=0nui2 and the products of the form unun+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 unun+1 as well as the product, unun+2. Further we give generating functions and combinatorial representations of the sums of squares of terms of {un} and the product, unun+2.