Crack-free Walls
Consider the problem of building a wall out of 2 1 and 3 1 bricks (horizontal vertical dimensions) such that, for extra strength, the gaps between horizontally-adjacent bricks never line up in consecutive layers, i.e. never form a "running crack".
For example, the following 9 3 wall is not acceptable due to the running crack shown in red:
There are eight ways of forming a crack-free 9 3 wall, written W(9,3) = 8.
Calculate W(32,10).