Enumeration of Polyominoes up to Size N=59

TL;DR

This paper extends the enumeration of polyominoes up to size 59, verifying previous counts and demonstrating that multi-threading significantly enhances computational efficiency in counting these shapes.

Contribution

It introduces optimized algorithms and multi-threading techniques to efficiently count polyominoes up to size 59, surpassing previous computational limits.

Findings

Verified counts for n <= 50 polyominoes

Computed new counts for n up to 59

Multi-threading improves counting efficiency

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.