Enumeration of L-convex polyominoes by rows and columns - Castiglione, G.; Frosini, A.; Restivo, A.; Rinaldi, S. (Theoretical computer science, 2005)
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once. Using the ECO method, we prove that the number f n of L-convex polyominoes with perimeter 2 ( n + 2 ) satisfies the rational recurrence relation f n = 4 f n - 1 - 2 f n - 2 , with f 0 = 1 , f 1 = 2 , f 2 = 7 . Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.