Enumeration of L-convex polyominoes by rows and columns

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in whichany two cells can be connected by a path of cells in the polyomino that switches direction betweenthe vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter2(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 presentsome open problems