arXiv math/06107342006-10math.CO

最后得分为n：n的[旧时代]篮球比赛的数量，其中主队从未输过，但也从未领先超过w分

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

备注：: 8 pages, no figures. Minor typos in equations for P_4, AZ_3 in Theorem 3, (38) and (39) corrected thanks to Pierre Lalonde
发表信息：: Electronic J. of Combinatorics 14(1) (2007), R19

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摘要：

本文证明了在0 <= y <= w的区域内，正方形格上从（0，0）到（2n，0）的步数为（1，1），（1，-1），（2，2）和（2，-2）的行走数的母函数（n）满足一个关于w的非常特殊的五阶非线性递归关系，这意味着它的分子和分母都满足一个线性递归关系.

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。