A319620 Number of connected antichain covers of n vertices by distinct sets whose dual is also a (not necessarily strict) antichain.

1, 1, 1, 2, 22, 2133

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

The a(4) = 22 antichain covers:
   {{1,2,3,4}}
   {{3,4},{1,2,3},{1,2,4}}
   {{2,4},{1,2,3},{1,3,4}}
   {{2,3},{1,2,4},{1,3,4}}
   {{1,4},{1,2,3},{2,3,4}}
   {{1,3},{1,2,4},{2,3,4}}
   {{1,2},{1,3,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4}}
   {{1,2},{1,4},{2,3},{3,4}}
   {{1,2},{1,3},{2,4},{3,4}}
   {{1,4},{2,4},{3,4},{1,2,3}}
   {{1,3},{2,3},{3,4},{1,2,4}}
   {{1,2},{2,3},{2,4},{1,3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4}}
   {{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, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

Sequence in context: A330124 A104149 A113761 * A054349 A182293 A222000

Adjacent sequences: A319617 A319618 A319619 * A319621 A319622 A319623

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved