A390165 Number of labeled semigroups with n elements satisfying the equation xyz = xy.

1, 1, 3, 10, 65, 856, 17497, 554632, 29533905, 2782465840, 486675409841, 167183253706624

Offset

0,3

Comments

A semigroup is an associative magma.

Links

Table of n, a(n) for n=0..11.

Index entries for sequences related to semigroups.

Example

The a(4) = 65 semigroups given by their Cayley tables are:
  1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1
  1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 3   2 2 2 2
  1 1 1 1   1 1 1 1   3 3 3 3   3 3 3 3   3 3 3 3   3 3 3 3
  1 1 1 1   4 4 4 4   3 3 3 3   4 4 4 4   4 4 4 4   4 4 4 4
    (4)       (12)      (12)      (12)      (24)      (1)

Crossrefs

Cf. A023814, A362386, A389829, A390163 (unlabeled version).

Sequence in context: A306187 A009400 A217388 * A004102 A072638 A262843

Adjacent sequences: A390162 A390163 A390164 * A390166 A390167 A390168

Keyword

nonn,more

Author

Andrew Howroyd, Nov 27 2025

Status

approved