A319621 Number of non-isomorphic connected antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

1, 1, 1, 2, 7, 73

Offset

0,4

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}}.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 antichain covers:
  {{1}}  {{1,2}}  {{1,2,3}}            {{1,2,3,4}}
                  {{1,2},{1,3},{2,3}}  {{1,2},{1,3,4},{2,3,4}}
                                       {{1,2},{1,3},{2,4},{3,4}}
                                       {{1,2},{1,3},{1,4},{2,3,4}}
                                       {{1,3},{1,4},{2,3},{2,4},{3,4}}
                                       {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
                                       {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Crossrefs

Cf. A006126, A007716, A007718, A049311, A056156, A059201, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

Sequence in context: A141315 A215637 A119811 * A167526 A064646 A366407

Adjacent sequences: A319618 A319619 A319620 * A319622 A319623 A319624

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved