M. Anđelić, C.M. da Fonseca, T. Koledin, Z. Stanić (2022) A second-order difference equation with sign-alternating coefficients, Kuwait Journal of Science, Vol. 50, No. 1, 10.48129/kjs.20425
Abstract. We provide an explicit solution for the terms of the sequence \((x_{n,k})\) defined by
x_{n,k}= x_{n-1,k} - (-1)^{\lfloor (n-2)/k\rfloor} x_{n-2,k} ,
for \(n\ge 3\), setting \(x_{1,k}=1\) and \(x_{2,k}=0\). Several particular examples are considered.