A351730 -id:A351730 - cp's OEIS frontend

A058158 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents and a fixed identity.

1, 1, 1, 1, 6, 4, 4, 45, 72, 35, 6, 528, 1308, 1676, 604, 80, 19935, 39700, 70170, 62060, 16727, 120, 3599436, 1969470, 3829000, 5167800, 3260382, 681232, 2760, 6085914205, 281840664, 294812385, 481221020, 482447637, 228315640, 38187291

Offset: 1

Christian G. Bower, Nov 14 2000

			Triangle begins:
   1;
   1,     1;
   1,     6,     4;
   4,    45,    72,    35;
   6,   528,  1308,  1676,   604;
  80, 19935, 39700, 70170, 62060, 16727;
  ...

Index entries for sequences related to monoids

Row sums give A058154.
Column 1: A058163.
Main diagonal is A351730(n-1).
Cf. A058137 (isomorphism classes), A058157, A058160 (commutative), A058166.

T(n,k) = A058157(n,k)/n.

a(30)-a(36) from Andrew Howroyd, Feb 15 2022

A058112 Number of isomorphism classes of idempotent semigroups of order n.

Original entry on oeis.org

1, 1, 3, 10, 46, 251, 1682, 13213, 119826, 1228712

Offset: 0

Christian G. Bower, Nov 09 2000

Main diagonal of A058108 and A058137.

Cf. A027851, A351730 (labeled).

Updated Feb 19 2001

a(8)-a(9) added by Andrew Howroyd, Feb 17 2022

A351731 Number of labeled idempotent monoids of order n.

Original entry on oeis.org

1, 2, 12, 140, 3020, 100362, 4768624, 305498328, 25293331098, 2619996058190

Offset: 1

Andrew Howroyd, Feb 17 2022

Main diagonal of A058157.

Cf. A058153, A351730.

a(n) = n * A351731(n-1).

cp's OEIS Frontend

A058158 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents and a fixed identity.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

Extensions

A058112 Number of isomorphism classes of idempotent semigroups of order n.

Views

Author

Keywords

Links

Crossrefs

Extensions

A351731 Number of labeled idempotent monoids of order n.

Views

Author

Keywords

Crossrefs

Formula