A319635 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

1, 1, 2, 3, 5, 7, 12, 16, 26, 36, 58

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(5) = 7 antichains:
1: {{1}}
2: {{1,2}}
   {{1},{2}}
3: {{1,2,3}}
   {{1},{2,3}}
   {{1},{2},{3}}
4: {{1,2,3,4}}
   {{1},{2,3,4}}
   {{1,2},{3,4}}
   {{1},{2},{3,4}}
   {{1},{2},{3},{4}}
5: {{1,2,3,4,5}}
   {{1},{2,3,4,5}}
   {{1,2},{3,4,5}}
   {{1},{2},{3,4,5}}
   {{1},{2,3},{4,5}}
   {{1},{2},{3},{4,5}}
   {{1},{2},{3},{4},{5}}

Crossrefs

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A308271 A360622 A275592 * A179822 A319769 A326083

Adjacent sequences: A319632 A319633 A319634 * A319636 A319637 A319638

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved