2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60367We study generating functions for the number of permutations in $\SS_n$ subject to two restrictions. One of the restrictions belongs to $\SS_3$, while the other to $\SS_k$. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.17 pages, 5 figuresCombinatorics05A05; 05A15; 30B70; 42C05text