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

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Volume14
Issue number1 R
DOIs
StatePublished - Jan 29 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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