A079197 -id:A079197 - cp's OEIS frontend

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

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

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

			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;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8)
C. van den Bosch, Closed binary operations on small sets

Row sums give A079199.

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

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

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

A079194 Number of isomorphism classes of non-associative non-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 2, 2, 0, 8, 66, 3115, 0, 1, 14, 18, 270, 467, 48260, 178888824

Offset: 0

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

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

			Triangle T(n,k) begins:
  0;
  0;
  2, 2;
  0, 8, 66, 3115;
  0, 1, 14, 18, 270, 467, 48260, 178888824;
  ...

C. van den Bosch, Closed binary operations on small sets
Index entries for sequences related to groupoids

Row sums give A079193.

Cf. A027423 (row lengths), A079171, A079192, A079197, A079200, A079201, A079210.

T(n,k) + A079197(n,k) + A079200(n,k) + A079201(n,k) = A079171(n,k).

A079192(n,k) = Sum_{k>=1} T(n,k)*A079210(n,k).

a(0)=0 prepended by Andrew Howroyd, Jan 26 2022

cp's OEIS Frontend

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

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