KöMaL 2026 B5518

Let $n$ and $k$ be positive integers. How many ways are there to partition the lattice trapezoid with vertices $(0,0)$, $(n,0)$, $(k,1)$ and $(0,1)$ into lattice triangles of area $1/2$? (A polygon is called a lattice polygon if both coordinates of all its vertices are integers.)