A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration

Mihai Ciucu, Christian Krattenthaler

We evaluate the determinant ${\det }_{1\le i,j\le n}((\genfrac{}{}{0ex}{}{x+y+j}{x-i+2j})-(\genfrac{}{}{0ex}{}{x+y+j}{x+i+2j}))$, which gives the number of lozenge tilings of a hexagon with cut off corners. A pa…