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.

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A079242 Number 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, 8, 2, 122, 2, 1682
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Cf. A079208, A079243 (isomorphism classes), A079230, A079232, A079234, A079236, A079195, A079240, A079244, A063524.

Formula

A079230(n) + A079232(n) + A079234(n) + A079236(n) + A079195(n) + A079240(n) + a(n) + A079244(n) + A063524(n) = A002489(n).
a(n) = Sum_{k>=1} A079208(n,k)*A079210(n,k).

Extensions

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

A079192 Number of non-associative non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 6, 18904, 4293916368, 298023193359221998, 10314424798468598595515695154, 256923577521058877628624940679487983651948, 6277101735386680763835789098689112757675628513119817261598
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Cf. A002489, A023813, A023814, A023815, A079193 (isomorphism classes), A079194, A079195, A079198.

Formula

a(n) + A079195(n) + A079198(n) + A023815(n) = A002489(n).
a(n) = Sum_{k>=1} A079194(n,k)*A079210(n,k).
a(n) = A002489(n) - A023813(n) - A023814(n) + A023815(n). - Andrew Howroyd, Jan 26 2022

Extensions

a(0)=0 prepended and a(5)-a(8) added by Andrew Howroyd, Jan 26 2022
Previous Showing 11-13 of 13 results.

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

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