Consider the problem of building a wall out of $2\times 1$ and $3\times 1$ bricks ($\text{horizontal}\times \text{vertical}$ 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 $9\times 3$ wall is not acceptable due to the running crack shown in red:

There are eight ways of forming a crack-free $9\times 3$ wall, written $W(9,3)=8$.

Calculate $W(32,10)$.