A319765 Number of non-isomorphic intersecting multiset partitions of weight n whose dual is also an intersecting multiset partition.

1, 1, 3, 6, 15, 31, 74, 156, 358, 792, 1821

Offset

0,3

Comments

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.

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) = 15 multiset partitions:
1: {{1}}
2: {{1,1}}
   {{1,2}}
   {{1},{1}}
3: {{1,1,1}}
   {{1,2,2}}
   {{1,2,3}}
   {{1},{1,1}}
   {{2},{1,2}}
   {{1},{1},{1}}
4: {{1,1,1,1}}
   {{1,1,2,2}}
   {{1,2,2,2}}
   {{1,2,3,3}}
   {{1,2,3,4}}
   {{1},{1,1,1}}
   {{1},{1,2,2}}
   {{2},{1,2,2}}
   {{3},{1,2,3}}
   {{1,1},{1,1}}
   {{1,2},{1,2}}
   {{1,2},{2,2}}
   {{1},{1},{1,1}}
   {{2},{2},{1,2}}
   {{1},{1},{1},{1}}

Crossrefs

Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.

Cf. A319752, A319766, A319767, A319768, A319769, A319773, A319774.

Sequence in context: A317792 A293732 A117161 * A244707 A244708 A244709

Adjacent sequences: A319762 A319763 A319764 * A319766 A319767 A319768

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved