A319644 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets.

1, 1, 2, 3, 5, 8, 18, 31, 73, 162, 413

Offset: 0

Author

Gus Wiseman, Sep 25 2018

Keywords

• nonn
• more

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.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 8 antichains:
1: {{1}}
2: {{1,1}}
   {{1},{2}}
3: {{1,1,1}}
   {{1},{2,2}}
   {{1},{2},{3}}
4: {{1,1,1,1}}
   {{1},{2,2,2}}
   {{1,1},{2,2}}
   {{1},{2},{3,3}}
   {{1},{2},{3},{4}}
5: {{1,1,1,1,1}}
   {{1},{2,2,2,2}}
   {{1,1},{1,2,2}}
   {{1,1},{2,2,2}}
   {{1},{2},{3,3,3}}
   {{1},{2,2},{3,3}}
   {{1},{2},{3},{4,4}}
   {{1},{2},{3},{4},{5}}
		

Crossrefs

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

Formula

Euler transform of A319629.