Enumeration of L-convex polyominoes by rows and columns

Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n+2) satisfies the rational recurrence relation fn=4fn-1-2fn-2, with f0=1, f1=2, f2=7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.