A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.

1, 1, 2, 3, 2, 0, 7, 15, 2, 0, 0, 7, 5, 0, 62, 112, 2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 4, 0, 48, 0, 0, 0, 0, 92, 0, 0, 42, 506, 0, 813, 32, 7397, 19684, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8

Offset

0,3

Comments

Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

Links

Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8; row 8 was derived from data given in the Distler-Kelsey reference)

C. van den Bosch, Closed binary operations on small sets

A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.

Index entries for sequences related to semigroups

Formula

A079174(n,k) + T(n,k) = A079171(n,k).

T(n, A027423(n)) = A058104(n).

A023814(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

Example

Triangle T(n,k) begins:
  1;
  1;
  2, 3;
  2, 0, 7, 15;
  2, 0, 0, 7, 5, 0, 62, 112;
  2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221;
  ...

Crossrefs

Row sums give A027851.

Cf. A023814, A027423 (row lengths), A079171, A079174, A079210.

Sequence in context: A011024 A105855 A152954 * A332742 A202815 A049336

Adjacent sequences: A079172 A079173 A079174 * A079176 A079177 A079178

Keyword

nonn,tabf

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Extensions

a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022

Status

approved