cp's OEIS Frontend

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.

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.

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%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