A318099 Number of non-isomorphic weight-n antichains of (not necessarily distinct) multisets whose dual is also an antichain of (not necessarily distinct) multisets.

1, 1, 4, 7, 19, 32, 81, 142, 337, 659, 1564

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

Crossrefs

Cf. A000219, A006126, A007716, A049311, A059201, A283877, A306007, A316980, A316983, A319558, A319560, A319616-A319646, A300913.

Sequence in context: A164265 A174465 A006381 * A274691 A102991 A298350

Adjacent sequences: A318096 A318097 A318098 * A318100 A318101 A318102

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved