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A385388 Irregular triangle read by rows: T(n,k) is the number of polysticks of size k, i.e., connected subsets of k edges, of the n X n flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= 2*n^2.

%I A385388 #6 Jun 29 2025 11:07:48
%S A385388 2,1,2,3,6,11,8,7,2,1,2,3,10,24,76,213,522,982,1308,1274,972,593,288,
%T A385388 114,38,10,2,1,2,3,10,28,104,387,1518,5799,21336,73400,230462,644155,
%U A385388 1556484,3151899,5183442,6823550,7342196,6639409,5131834,3433229,1992710,1007190,440148,166572,53566,14806,3356,682,104,20,2,1
%N A385388 Irregular triangle read by rows: T(n,k) is the number of polysticks of size k, i.e., connected subsets of k edges, of the n X n flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= 2*n^2.
%F A385388 T(n,k) <= 2*A385390(n,k), with equality if and only if k is odd.
%e A385388 Triangle begins:
%e A385388   2, 1;
%e A385388   2, 3,  6, 11,  8,   7,   2,   1;
%e A385388   2, 3, 10, 24, 76, 213, 522, 982, 1308, 1274, 972, 593, 288, 114, 38, 10, 2, 1;
%e A385388   ...
%Y A385388 Cf. A385383 (polyominoes), A385387 (row sums), A385390 (interchange of rows and columns of the torus allowed).
%K A385388 nonn,tabf
%O A385388 1,1
%A A385388 _Pontus von Brömssen_, Jun 27 2025