A079201 Number of isomorphism classes of associative commutative closed binary operations on a set of order n, listed by class size.

1, 1, 0, 3, 0, 0, 3, 9, 0, 0, 0, 3, 0, 0, 16, 39, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 4, 91, 0, 55, 0, 715, 1258, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12

Offset

0,4

Comments

Number of 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)

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

Index entries for sequences related to semigroups

Formula

A079194(n,k) + A079197(n,k) + A079200(n,k) + T(n,k) = A079171(n,k).

T(n, A027423(n)) = A058105(n).

A023815(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

Example

Triangle T(n,k) begins:
  1;
  1;
  0, 3;
  0, 0, 3, 9;
  0, 0, 0, 3, 0, 0, 16, 39;
  0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201;

Crossrefs

Row sums are A001426.

Cf. A023815, A027423 (row lengths), A079171, A079194, A079197, A079200, A058105.

Sequence in context: A151665 A171793 A079209 * A279368 A021773 A244126

Adjacent sequences: A079198 A079199 A079200 * A079202 A079203 A079204

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