Question 8
Let $n \geq 1$ be an integer. How many ways can the rectangle having vertices $(0,0)$, $(n, 0)$, $(n, 1)$, $(0,1)$ be dissected into $2n$ triangles, all vertices of which have integer coordinates?
The triangles are considered as positioned on the coordinate plane; in particular, tilings related by rotation and reflection are considered distinct.
The triangles are considered as positioned on the coordinate plane; in particular, tilings related by rotation and reflection are considered distinct.