2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61980We study generating functions for the number of permutations in $S_n$ subject to set of restrictions. One of the restrictions belongs to $S_3$, while the others to $S_k$. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind.9 pagesCombinatorics05A05; 05A15; 30B70; 42C05text