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 1-5 of 5 results.

A079197 Number of isomorphism classes of non-associative commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 1, 1, 4, 5, 107, 0, 0, 0, 5, 0, 28, 488, 43389
Offset: 1

Views

Author

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

Keywords

Comments

A079194(n)+A079197(n)+A079200(n)+A079201(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; 0,1; 1,4,5,107; 0,0,0,5,0,28,488,43389
A079195(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 A079196(x).

Links

Crossrefs

Cf. A079194, A079198, A079199, A079200, A079201.

A079199 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 2, 12, 130, 1590, 26491, 1610381, 3683808612, 105978166390449
Offset: 1

Views

Author

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

Keywords

Comments

A079193(n)+A079196(n)+A079199(n)+A001426(n)=A001329(n).
Each a(n) is equal to the sum of the elements in row n of A079200.
Since this is the number of nonisomorphic noncommutative semigroups of order n, A079199(n)=A027851(n)-A001426(n). - Stanislav Sykora, Apr 03 2016

Links

Crossrefs

Cf. A001426, A027851, A079193, A079196, A079198, A079200.

Extensions

Added terms a(5)-a(9). - Stanislav Sykora, Apr 03 2016

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

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

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

Examples

			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;

Links

Crossrefs

Row sums are A001426.
Cf. A023815, A027423 (row lengths), A079171, A079194, A079197, A079200, A058105.

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).

Extensions

a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022

A079198 Number of associative non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 2, 50, 2352, 153002, 15876046, 7676692858
Offset: 1

Views

Author

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

Keywords

Comments

a(n) + A079192(n) + A079195(n) + A023815(n) = A002489(n).
Each a(n) is equal to the sum of the products of each element in row n of A079200 and the corresponding element of A079210.
Since this is the number of labeled noncommutative semigroups on an n-set, a(n) = A023814(n)-A023815(n). - Stanislav Sykora, Apr 03 2016

Links

Crossrefs

Cf. A023814, A023815, A079192, A079195, A079199, A079200.

Extensions

a(5)-a(7) added by Stanislav Sykora, Apr 03 2016

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

Views

Author

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

Keywords

Comments

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

Examples

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

Links

Crossrefs

Row sums give A079193.
Cf. A027423 (row lengths), A079171, A079192, A079197, A079200, A079201, A079210.

Formula

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).

Extensions

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

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