This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385381 #6 Jun 29 2025 11:08:19 %S A385381 1,2,5,3,10,28,4,21,102,801,5,40,382,6790,129550,6,86,1788,68569, %T A385381 2694721 %N A385381 Triangle read by rows: T(n,k) is the number of polyominoes, i.e., connected nonempty subsets of square cells (or vertices), of the n X k flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= n. %C A385381 Two square cells are connected if they share an edge. %C A385381 Subsets that differ by interchanging rows and columns (when n = k) are considered distinct. For example, there are two polyominoes of size 2 when 2 <= k <= n, one horizontal and one vertical. See A385384 for the analog of the main diagonal of this sequence in the case where such subsets are considered identical. %H A385381 Pontus von Brömssen, <a href="/A385381/a385381.png">Illustration for T(3,3)</a>. %e A385381 Triangle begins: %e A385381 n\k| 1 2 3 4 5 6 %e A385381 ---+--------------------------- %e A385381 1 | 1 %e A385381 2 | 2 5 %e A385381 3 | 3 10 28 %e A385381 4 | 4 21 102 801 %e A385381 5 | 5 40 382 6790 129550 %e A385381 6 | 6 86 1788 68569 2694721 ? %Y A385381 Cf. A385382 (main diagonal), A385384, A385386 (edge subsets). %K A385381 nonn,tabl,more %O A385381 1,2 %A A385381 _Pontus von Brömssen_, Jun 27 2025