On the Counting Sequence of Z-convex Polyominoes

Abstract

The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper, we present a set of formulas and equations that are the basis of a C++ program that allows you to compute the longest counting sequence known to date (with respect to the area) of convex polyominoes of degree of convexity at most 2