2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60299We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, 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 non-automatic fashion.14 pages, AmS-TeX, uses TeXDraw; minor modificationsCombinatoricsClassical Analysis and ODEs05A15 (Primary) 05A16 05A17 05A19 05B45 33C20 52C20 (Secondary)text