A319779 Number of intersecting multiset partitions of weight n whose dual is not an intersecting multiset partition.

1, 0, 0, 0, 1, 4, 20, 66, 226, 696, 2156

Offset

0,6

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}}.

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

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.

Links

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

Example

Non-isomorphic representatives of the a(4) = 1 through a(6) = 20 multiset partitions:
4: {{1,3},{2,3}}
5: {{1,2},{2,3,3}}
   {{1,3},{2,3,3}}
   {{1,4},{2,3,4}}
   {{3},{1,3},{2,3}}
6: {{1,2},{2,3,3,3}}
   {{1,3},{2,2,3,3}}
   {{1,3},{2,3,3,3}}
   {{1,3},{2,3,4,4}}
   {{1,4},{2,3,4,4}}
   {{1,5},{2,3,4,5}}
   {{1,1,2},{2,3,3}}
   {{1,2,2},{2,3,3}}
   {{1,2,3},{3,4,4}}
   {{1,2,4},{3,4,4}}
   {{1,2,5},{3,4,5}}
   {{1,3,3},{2,3,3}}
   {{1,3,4},{2,3,4}}
   {{2},{1,2},{2,3,3}}
   {{3},{1,3},{2,3,3}}
   {{4},{1,4},{2,3,4}}
   {{1,3},{2,3},{2,3}}
   {{1,3},{2,3},{3,3}}
   {{1,4},{2,4},{3,4}}
   {{3},{3},{1,3},{2,3}}

Crossrefs

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

Cf. A319775, A319778, A319781, A319783.

Sequence in context: A194094 A055538 A302317 * A287244 A344993 A123613

Adjacent sequences: A319776 A319777 A319778 * A319780 A319781 A319782

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved