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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.
0
1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 2, 1, 1, 7, 56, 317, 1524, 5733, 17728, 44767, 94427, 166786, 249624, 316950, 343424, 316950, 249624, 166786, 94427, 44767, 17728, 5733, 1524, 317, 56, 7, 1, 1, 23, 1012, 36125, 1035496, 23878229, 456936220, 7437730463
OFFSET
0,9
COMMENTS
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.
T(n,k) is the number of symmetry classes of subsets of size k from S_n.
LINKS
Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
FORMULA
T(n,k) = 1/8 * (C(n,k) + 2*A277080(n,k) + 2*A277081(n,k) + 2*A277085(n,k) + A277083(n,k)).
EXAMPLE
Triangle starts:
1, 1;
1, 1;
1, 1, 1;
1, 2, 5, 5, 5, 2, 1;
CROSSREFS
Rows lengths give A038507.
Sequence in context: A363764 A116698 A246900 * A229710 A240947 A023398
KEYWORD
nonn,tabf
AUTHOR
Christian Bean, Sep 28 2016
STATUS
approved