# Problem 215: Crack-free Walls

![graphic](img215.gif)

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).