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.

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

Table of n, a(n) for n=0..46.

Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, 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.

Cf. A277080, A277081, A277083, A277085.

Sequence in context: A363764 A116698 A246900 * A229710 A240947 A023398

Adjacent sequences: A277083 A277084 A277085 * A277087 A277088 A277089

Keyword

nonn,tabf

Author

Christian Bean, Sep 28 2016

Status

approved