2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70519The sequence of period 6 starting with 1, 1, 0, -1, -1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, and their relations with Euler's pentagonal numbers theorem and Chebyshev polynomials are discussed.Archive version is already official. Published by JNMP at http://www.sm.luth.se/math/JNMP/Combinatoricstext