A058108 Triangle read by rows: number of nonisomorphic semigroups of order n with k idempotents.

1, 2, 3, 5, 9, 10, 20, 50, 72, 46, 171, 309, 590, 594, 251, 5284, 2806, 5422, 7772, 5668, 1682, 1224331, 58583, 61323, 101539, 109107, 59576, 13213, 3667785000, 9207430, 1150085, 1466691, 1983558, 1626956, 690871, 119826, 105952488687468, 25412267163, 136799017, 27690828, 36991211, 39865274, 25666762, 8739857, 1228712

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).

A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.

Index entries for sequences related to semigroups

Example

Triangle begins:
    1;
    2,   3;
    5,   9,  10;
   20,  50,  72,  46;
  171, 309, 590, 594, 251;
  ...

Crossrefs

Row sums give A027851. Main diagonal: A058112. Columns 1-3: A058109-A058111.

Sequence in context: A303435 A090845 A262990 * A174512 A056144 A284626

Adjacent sequences: A058105 A058106 A058107 * A058109 A058110 A058111

Keyword

nonn,tabl,hard

Author

Christian G. Bower, Nov 09 2000

Extensions

Updated Feb 19 2001

More terms from Andreas Distler, Jan 13 2011

Status

approved