You have $N$ bricks two dimensional bricks of the dimension $1 \times 2$. The bricks are rotatable i.e. you can turn the brick of dimension $1 \times 2$ into $2 \times 1$. Now, you have to determine how many different rectangular shapes can you create by arranging the bricks. Two rectangular shapes are different if their dimensions are different. There should be no space left in the rectangular shapes that you create with the bricks i.e they must be filled with bricks.
This is a companion discussion topic for the original entry at https://toph.co/p/arrange-the-bricks