cp's OEIS Frontend

A385383 Irregular triangle read by rows: T(n,k) is the number of polyominoes of size k, i.e., connected subsets of k square cells (or vertices), of the n X n flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= n^2.

%I A385383 #5 Jun 29 2025 11:07:29
%S A385383 1,1,2,1,1,1,2,3,5,6,6,3,1,1,1,2,3,9,17,44,81,150,163,161,88,56,16,8,
%T A385383 1,1,1,2,3,9,21,62,168,490,1324,3370,7433,13905,20961,24927,23008,
%U A385383 16766,9825,4669,1831,576,157,32,8,1,1
%N A385383 Irregular triangle read by rows: T(n,k) is the number of polyominoes of size k, i.e., connected subsets of k square cells (or vertices), of the n X n flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= n^2.
%H A385383 Pontus von Brömssen, <a href="/A385381/a385381.png">Illustration for row n = 3</a>.
%F A385383 T(n,k) = A056780(k) if n >= k.
%F A385383 T(n,k) <= 2*A385385(n,k), with equality if and only if k = 2.
%e A385383 Triangle begins:
%e A385383   1;
%e A385383   1, 2, 1, 1;
%e A385383   1, 2, 3, 5,  6,  6,  3,   1,   1;
%e A385383   1, 2, 3, 9, 17, 44, 81, 150, 163, 161, 88, 56, 16, 8, 1, 1;
%e A385383   ...
%Y A385383 Cf. A056780, A385382 (row sums), A385385 (interchange of rows and columns of the torus allowed), A385388 (edge subsets).
%K A385383 nonn,tabf
%O A385383 1,3
%A A385383 _Pontus von Brömssen_, Jun 27 2025