A256039 Triangle read by rows: number of idempotents of rank k in partial Brauer monoid PB_n.

1, 1, 1, 4, 2, 1, 16, 18, 3, 1, 100, 88, 48, 4, 1, 676, 860, 280, 100, 5, 1, 5776, 6696, 4020, 680, 180, 6, 1, 53824, 76552, 35196, 13580, 1400, 294, 7, 1, 583696, 805568, 531328, 131936, 37240, 2576, 448, 8, 1, 6864400, 10765008, 6159168, 2571744, 397656, 88200, 4368, 648, 9, 1, 90174016, 141145120, 101644560, 32404800, 9780960, 1027152, 187320, 6960, 900, 10, 1

Offset

0,4

Links

Table of n, a(n) for n=0..65.

I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014.

Example

Triangle begins:
1,
1, 1,
4, 2, 1,
16, 18, 3, 1,
100, 88, 48, 4, 1,
676, 860, 280, 100, 5, 1,
5776, 6696, 4020, 680, 180, 6, 1,
53824, 76552, 35196, 13580, 1400, 294, 7, 1,
583696, 805568, 531328, 131936, 37240, 2576, 448, 8, 1,
6864400, 10765008, 6159168, 2571744, 397656, 88200, 4368, 648, 9, 1,
90174016, 141145120, 101644560, 32404800, 9780960, 1027152, 187320, 6960, 900, 10, 1,
...

Crossrefs

Sequence in context: A236830 A269736 A264535 * A152391 A144088 A039948

Adjacent sequences: A256036 A256037 A256038 * A256040 A256041 A256042

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 14 2015

Status

approved