The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124816We show that the generating function (in n) for the number of walks on the square lattice with steps (1,1), (1,-1), (2,2) and (2,-2) from (0,0) to (2n,0) in the region 0 <= y <= w satisfies a very special fifth order nonlinear recurrence relation in w that implies both its numerator and denominator satisfy a linear recurrence relation.8 pages, no figures. Minor typos in equations for P_4, AZ_3 in Theorem 3, (38) and (39) corrected thanks to Pierre LalondeCombinatorics05A15The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Pointstext