A closed formula for the number of convex permutominoes (Q1010614)

Summary: We determine a closed formula for the number of convex permutominoes of size \(n\). We reach this goal by providing a recursive generation of all convex permutominoes of size \(n+1\) from the objects of size \(n\), according to the ECO method, and then translating this construction into a system of functional equations satisfied by the generating function of convex permutominoes. As a consequence we easily obtain also the enumeration of some classes of convex polyominoes, including stack and directed convex permutominoes.