Enumeration of Polyominoes up to Size N=59

Abstract: This paper reports the results of numerical computations for determining the number of polyominoes of size n (n-ominoes). We verify the existing counts for n <= 50 and newly compute the total number of polyominoes up to n <= 59, extending the counting limit. This work shows that, in addition to optimizing the search algorithm for the polyomino counting problem, multi-threading dramatically improves computational efficiency.