The Number of [Old-Time] Basketball Games with Final Score n: n where the Home Team was Never Losing but also Never Ahead by Mor

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 satisfies a very special fifth order nonlinear recurrence relation in w that implies both its numerator and denominator satisfy a linear recurrence relation. 1 

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Arvind Ayyer, Doron Zeilberger
• Keywords: COMBINATORICS 2007, Generating Function, Recurrence Relation, Square Lattice