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 1-2 of 2 results.

A023815 Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.

Original entry on oeis.org

1, 1, 6, 63, 1140, 30730, 1185072, 66363206, 7150843144, 3829117403448
Offset: 0

Views

Author

Lyle Ramshaw (ramshaw(AT)pa.dec.com)

Keywords

Links

Crossrefs

Row sums of A058167.
Cf. A001423, A001426 (isomorphism classes), A023813 (commutative only), A023814 (associative only), A027851.
Cf. A002489, A079192, A079195, A079198, A079201, A079210.

Formula

a(n) + A079192(n) + A079195(n) + A079198(n) = A002489(n).
a(n) = Sum_{k>=1} A079201(n,k)*A079210(n,k). - Andrew Howroyd, Jan 26 2022

Extensions

a(8) from Andrew Howroyd, Jan 26 2022
a(9) from Andrew Howroyd, Feb 14 2022

A058116 Triangle read by rows: T(n,k) is the number of isomorphism classes of commutative semigroups of order n with k idempotents.

Original entry on oeis.org

1, 2, 1, 5, 5, 2, 16, 23, 14, 5, 62, 106, 93, 49, 15, 342, 544, 582, 422, 200, 53, 3435, 3380, 3773, 3360, 2178, 943, 222, 97061, 30788, 27222, 26625, 21283, 12676, 5072, 1078
Offset: 1

Views

Author

Christian G. Bower, Nov 09 2000

Keywords

Examples

			Triangle begins:
   1;
   2,   1;
   5,   5,  2;
  16,  23, 14,  5;
  62, 106, 93, 49, 15;
  ...

Links

Crossrefs

Row sums give A001426.
Main diagonal is A006966(n+1).
Column 1 is A058117.
The labeled version is A058167.
Cf. A058108, A058142.

Extensions

a(29)-a(36) from Andrew Howroyd, Jan 27 2022
Showing 1-2 of 2 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.