Kilic, Nayil2025-03-232025-03-2320190381-7032https://hdl.handle.net/11486/7370In this paper, we consider the generalized Fibonacci sequence {u(n)}. We derive a generating matrix for both the sums of squares of the form Sigma(n)(k=0) q(n-k)u(k)(2) (q not equal 0) and the products of the form qu(n)u(n+2) (q not equal 0). Also, we give a matrix method to generate the sums of product of two consecutive terms u(n)n(n+1), as well as the product qu(n)u(n+2) (q not equal 0). Furthermore we obtain generating functions and combinatorial representations of u(n)u(n+1) and u(n-1)u(n+1).eninfo:eu-repo/semantics/closedAccessmatrix methodsgenerating functionFibonacci numbersArticle146243254Q4WOS:000478701200019N/A