cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A079209 Number of isomorphism classes of associative commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 3, 0, 0, 3, 9, 0, 0, 0, 3, 0, 0, 16, 39
Offset: 1

Views

Author

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

Keywords

Comments

A079202(n)+A079203(n)+A079204(n)+A079205(n)+A079197(n)+A079207(n)+A079208(n)+A079209(n)+A063524(n)=A079171(n)
Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
First four rows: 0; 0,3; 0,0,3,9; 0,0,0,3,0,0,16,39
A079244(x) is equal to the sum of the products of each element in row x of this sequence and the corresponding element of A079210.
The sum of each row x of this sequence is given by A079245(x).

Links

Crossrefs

Cf. A079202, A079203, A079204, A079205, A079197, A079207, A079208, A079244, A079245.

A079231 Number of isomorphism classes of non-associative non-commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 2187, 147067071
Offset: 1

Views

Author

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

Keywords

Comments

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)
Each a(n) is equal to the sum of the elements in row n of A079202.

Crossrefs

Cf. A079202, A079230, A079233, A079235, A079237, A079196, A079241, A079243, A079245, A063524.

A079233 Number of isomorphism classes of non-associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 2, 992, 31853003
Offset: 1

Views

Author

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

Keywords

Comments

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)
Each a(n) is equal to the sum of the elements in row n of A079203.

Crossrefs

Cf. A079203, A079232, A079231, A079235, A079237, A079196, A079241, A079243, A079245, A063524.

A079235 Number of isomorphism classes of non-associative non-commutative anti-associative non-anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 8, 13138
Offset: 1

Views

Author

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

Keywords

Comments

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)
Each a(n) is equal to the sum of the elements in row n of A079204.

Crossrefs

Cf. A079204, A079234, A079231, A079233, A079237, A079196, A079241, A079243, A079245, A063524.

A079237 Number of isomorphism classes of non-associative non-commutative anti-associative anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 2, 2, 4642
Offset: 1

Views

Author

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

Keywords

Comments

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)
Each a(n) is equal to the sum of the elements in row n of A079205.

Crossrefs

Cf. A079205, A079236, A079231, A079233, A079235, A079196, A079241, A079243, A079245, A063524.

A079244 Number of associative commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 6, 63, 1140
Offset: 1

Views

Author

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

Keywords

Comments

A079230(n)+A079232(n)+A079234(n)+A079236(n)+A079195(n)+A079240(n)+A079242(n)+A079244(n)+A063524(n)=A002489(n)
Each a(n) is equal to the sum of the products of each element in row n of A079209 and the corresponding element of A079210.

Links

Crossrefs

Cf. A079209, A079245, A079230, A079232, A079234, A079236, A079195, A079240, A079242, A063524.

A079241 Number of isomorphism classes of associative non-commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 0, 10, 127, 1588, 26487, 1610379, 3683808608
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Row sums of A079207.
Cf. A079240 (labeled case), A079231, A079233, A079235, A079237, A079196, A079243, A079245, A063524.

Formula

A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + a(n) + A079243(n) + A079245(n) + A063524(n) = A002489(n).
a(n) = A027851(n) - A001426(n) - A079243(n). - Andrew Howroyd, Jan 27 2022

Extensions

a(0)=0 prepended and a(5)-a(8) added by Andrew Howroyd, Jan 27 2022

A079243 Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 2, 2, 3, 2, 4, 2, 4
Offset: 0

Views

Author

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

Keywords

Comments

The only closed binary operations that are both commutative and anti-commutative are those on sets of size <= 1. The significance of non-commutative (and non-anti-associative) in the name is that it excludes this possibility. Otherwise, the first two terms would be 1. - Andrew Howroyd, Jan 26 2022

Examples

			From _Andrew Howroyd_, Jan 26 2022: (Start)
The a(6) = 4 operations are the two shown below and their converses.
    | 1 2 3 4 5 6         | 1 2 3 4 5 6
  --+------------       --+------------
  1 | 1 2 3 4 5 6       1 | 1 2 3 1 2 3
  2 | 1 2 3 4 5 6       2 | 1 2 3 1 2 3
  3 | 1 2 3 4 5 6       3 | 1 2 3 1 2 3
  4 | 1 2 3 4 5 6       4 | 4 5 6 4 5 6
  5 | 1 2 3 4 5 6       5 | 4 5 6 4 5 6
  6 | 1 2 3 4 5 6       6 | 4 5 6 4 5 6
(End)

Links

Crossrefs

Row sums of A079208.
Cf. A079242 (labeled case), A079231, A079233, A079235, A079237, A079196, A079241, A079245, A063524.

Formula

A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + A079241(n) + a(n) + A079245(n) + A063524(n) = A002489(n).
Conjecture: a(n) = A000005(n) for n > 1. - Andrew Howroyd, Jan 26 2022

Extensions

a(0)=0 prepended and a(5)-a(8) from Andrew Howroyd, Jan 26 2022
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.