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
A Ayyer, D Zeilberger - arXiv preprint math/0610734, 2006 - arxiv.org
A Ayyer, D Zeilberger
arXiv preprint math/0610734, 2006•arxiv.orgWe 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.
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.
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.
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