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

Arvind Ayyer, Doron Zeilberger

We 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…