Some New Finite Sums Involving Generalized Fibonacci and Lucas Numbers

Abstract

In this paper, we compute various finite sums that alternate according to \((-1)^{\binom{n}{k}}\) involving the generalized Fibonacci and Lucas numbers for \(k = 3, 4, 5\) and even \(k\) of the form \(2^m\) with \(m \geq 1\).