A319637 Number of non-isomorphic T_0-covers of n vertices by distinct sets.

1, 1, 3, 29, 1885, 18658259

Offset

0,3

Comments

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict (no repeated elements).

Links

Table of n, a(n) for n=0..5.

Example

Non-isomorphic representatives of the a(3) = 29 covers:
   {{1,3},{2,3}}
   {{1},{2},{3}}
   {{1},{3},{2,3}}
   {{2},{3},{1,2,3}}
   {{2},{1,3},{2,3}}
   {{3},{1,3},{2,3}}
   {{3},{2,3},{1,2,3}}
   {{1,2},{1,3},{2,3}}
   {{1},{2},{3},{2,3}}
   {{1,3},{2,3},{1,2,3}}
   {{1},{2},{3},{1,2,3}}
   {{1},{2},{1,3},{2,3}}
   {{2},{3},{1,3},{2,3}}
   {{1},{3},{2,3},{1,2,3}}
   {{2},{3},{2,3},{1,2,3}}
   {{3},{1,2},{1,3},{2,3}}
   {{2},{1,3},{2,3},{1,2,3}}
   {{3},{1,3},{2,3},{1,2,3}}
   {{1},{2},{3},{1,3},{2,3}}
   {{1,2},{1,3},{2,3},{1,2,3}}
   {{1},{2},{3},{2,3},{1,2,3}}
   {{2},{3},{1,2},{1,3},{2,3}}
   {{1},{2},{1,3},{2,3},{1,2,3}}
   {{2},{3},{1,3},{2,3},{1,2,3}}
   {{3},{1,2},{1,3},{2,3},{1,2,3}}
   {{1},{2},{3},{1,2},{1,3},{2,3}}
   {{1},{2},{3},{1,3},{2,3},{1,2,3}}
   {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
   {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A006126, A007716, A049311, A059201, A283877, A316980, A316983, A318099, A319558, A319559, A319616-A319646, A300913.

Sequence in context: A162085 A182385 A255597 * A003190 A322451 A213792

Adjacent sequences: A319634 A319635 A319636 * A319638 A319639 A319640

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Extensions

a(5) from Max Alekseyev, Jul 13 2022

Status

approved