A079207 Number of isomorphism classes of associative non-commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n, listed by class size.

0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 4, 4, 0, 46, 73, 0, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 36, 0, 0, 0, 0, 84, 0, 0, 38, 415, 0, 758, 32, 6682, 18426, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8

Offset

0,7

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)

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

Index entries for sequences related to semigroups

Formula

A079202(n,k) + A079203(n,k) + A079204(n,k) + A079205(n,k) + A079197(n,k) + A079208(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).

A079240(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

T(n,k) = A079175(n,k) - A079201(n,k) - A079208(n,k). - Andrew Howroyd, Jan 27 2022

Example

Triangle T(n,k) begins:
  0;
  0;
  0, 0;
  0, 0, 4, 6;
  0, 0, 0, 4, 4, 0, 46, 73;
  0, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
  ...

Crossrefs

Row sums give A079241.

Cf. A027423 (row lengths), A079175, A079201, A079202, A079203, A079204, A079205, A079197, A079208, A079209, A079240.

Sequence in context: A231407 A005927 A201529 * A259825 A276449 A056945

Adjacent sequences: A079204 A079205 A079206 * A079208 A079209 A079210

Keyword

nonn,tabf

Author

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

Extensions

a(0)=0 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 27 2022

Status

approved