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{\bf Arvind Ayyer and Doron Zeilberger}
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{\bf 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}
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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 $0 \leq y \leq w$ satisfies a
very special fifth order \emph{nonlinear} recurrence relation in $w$
that implies both its numerator and denominator satisfy a
\emph{linear} recurrence relation.
\bye