A second-order difference equation with sign-alternating coefficients: DOI : 10.48129/kjs.20425 - Fonseca, Prof.Carlos; Kizilates, Can; Terzioglu, Nazlihan (Kuwait Journal of Science, 2023)
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 $n\geqslant 3$, setting $x_{1,k}=1$ and $x_{2,k}=0$. Several particular examples are considered.