2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66424Let $w_{n+2}=pw_{n+1}+qw_{n}$ for $n\geq0$ with $w_0=a$ and $w_1=b$. In this paper we find an explicit expression, in terms of determinants, for $\sum_{n\geq0} w_n^kx^n$ for any $k\geq1$. As a consequence, we derive all the previously known results for this kind of problems, as well as many new results.5 pagesCombinatoricstext