Sums of the \(AB\)-Generalized Fibonacci Sequence

Abstract

In this short paper, we introduce the second order linear recurrence relation of the \(AB\)-generalized Fibonacci sequence and give the explicit formulas for the sums of the positively and negatively subscripted terms of the \(AB\)-generalized Fibonacci sequence by matrix methods. This sum generalizes the one obtained earlier by Kilig in \([2]\).