How is this recursion for horizontally convex polyominoes clear according to author? 
How is the recursion $a(m,n)$ clear? I don't understand how this is clear.

Community wiki answer so the question can be marked as answered:
As noted by achille hui in a comment, $l$ is the number of squares in the layer next to the bottom layer. The polyomino without the bottom layer contains $n-m$ squares and can thus take $a(l,n-m)$ forms, and it can be placed in $m+l-1$ different horizontal locations such that the $m$ squares in the bottom layer and the $l$ squares in the next layer overlap in at least one square.
