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A277086 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n with respect to the symmetries of the square.

%I A277086 #26 Jul 22 2024 09:47:36
%S A277086 1,1,1,1,1,1,1,1,2,5,5,5,2,1,1,7,56,317,1524,5733,17728,44767,94427,
%T A277086 166786,249624,316950,343424,316950,249624,166786,94427,44767,17728,
%U A277086 5733,1524,317,56,7,1,1,23,1012,36125,1035496,23878229,456936220,7437730463
%N A277086 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n with respect to the symmetries of the square.
%C A277086 A permutation, p, can be thought of as a set of points (i, p(i)). In this viewpoint it is natural to consider the symmetries of the square.
%C A277086 T(n,k) is the number of symmetry classes of subsets of size k from S_n.
%H A277086 Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://doi.org/10.37236/12686">Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding</a>, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); <a href="https://arxiv.org/abs/2312.07716">arXiv preprint</a>, arXiv:2312.07716 [math.CO], 2023.
%F A277086 T(n,k) = 1/8 * (C(n,k) + 2*A277080(n,k) + 2*A277081(n,k) + 2*A277085(n,k) + A277083(n,k)).
%e A277086 Triangle starts:
%e A277086 1, 1;
%e A277086 1, 1;
%e A277086 1, 1, 1;
%e A277086 1, 2, 5, 5, 5, 2, 1;
%Y A277086 Rows lengths give A038507.
%Y A277086 Cf. A277080, A277081, A277083, A277085.
%K A277086 nonn,tabf
%O A277086 0,9
%A A277086 _Christian Bean_, Sep 28 2016