Question 150
Let $n \geq 1$ be a positive integer. A square of side length $n$ is divided by lines parallel to each side into $n^{2}$ squares of side length $1$. Find the number of parallelograms which have vertices among the vertices of the $n^{2}$ squares of side length $1$, with both sides smaller or equal to $2$, and which have the area equal to $2$.