A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size.

0, 0, 2, 0, 2, 0, 4, 6, 2, 0, 0, 4, 5, 0, 46, 73, 2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 36, 0, 0, 0, 0, 86, 0, 0, 38, 415, 0, 758, 32, 6682, 18426, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8

Offset

0,3

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

Formula

A079194(n,k) + A079197(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).

A079198(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

T(n,k) = A079175(n,k) - A079201(n,k). - Andrew Howroyd, Jan 26 2022

Example

Triangle T(n,k) begins:
  0;
  0;
  2, 0;
  2, 0, 4, 6;
  2, 0, 0, 4, 5, 0, 46, 73;
  2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
  ...

Crossrefs

Row sums give A079199.

Cf. A027423 (row lengths), A079171, A079194, A079175, A079197, A079198, A079199, A079201, A079210.

Sequence in context: A288182 A072680 A067770 * A011420 A035686 A308214

Adjacent sequences: A079197 A079198 A079199 * A079201 A079202 A079203

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 26 2022

Status

approved