2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160358There is a strikingly simple classical formula for the number of lattice paths avoiding the line x = ky when k is a positive integer. We show that the natural generalization of this simple formula continues to hold when the line x = ky is replaced by certain periodic staircase boundaries--but only under special conditions. The simple formula fails in general, and it remains an open question to what extent our results can be further generalized.Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs addedCombinatorics05A15text