Abstract. We evaluate the determinant

det_{1≤i,j≤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 nonautomatic fashion.