A319632 Number of non-isomorphic weight-n antichains of (not necessarily distinct) sets whose dual is also an antichain of (not necessarily distinct) sets.

1, 1, 3, 5, 11, 17, 35, 53, 100, 154, 275

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 weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

Table of n, a(n) for n=0..10.

Example

Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 set systems:
1: {{1}}
2: {{1,2}}
   {{1},{1}}
   {{1},{2}}
3: {{1,2,3}}
   {{1},{2,3}}
   {{1},{1},{1}}
   {{1},{2},{2}}
   {{1},{2},{3}}
4: {{1,2,3,4}}
   {{1},{2,3,4}}
   {{1,2},{1,2}}
   {{1,2},{3,4}}
   {{1},{1},{2,3}}
   {{1},{2},{3,4}}
   {{1},{1},{1},{1}}
   {{1},{1},{2},{2}}
   {{1},{2},{2},{2}}
   {{1},{2},{3},{3}}
   {{1},{2},{3},{4}}

Crossrefs

Cf. A006126, A007716, A049311, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A147071 A006171 A261674 * A060647 A320353 A155989

Adjacent sequences: A319629 A319630 A319631 * A319633 A319634 A319635

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved