A nonautomatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration
Abstract
We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{xi+2j}\binom{x+y+j}{x+i+2j})$, which gives the number of lozenge tilings of a hexagon with cut off corners. A particularly interesting feature of this evaluation is that it requires the proof of a certain hypergeometric identity which we accomplish by using Gosper's algorithm in a nonautomatic fashion.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:math/0011047
 Bibcode:
 2000math.....11047C
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Classical Analysis and ODEs;
 05A15 (Primary) 05A16 05A17 05A19 05B45 33C20 52C20 (Secondary)
 EPrint:
 14 pages, AmSTeX, uses TeXDraw