A319755 Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n.

1, 1, 2, 3, 6, 9, 19, 30, 60, 107, 212

Offset

0,3

Comments

A set multipartition is intersecting if no two parts are disjoint. The weight of a set multipartition 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) = 9 set multipartitions:
1: {{1}}
2: {{1,2}}
   {{1},{1}}
3: {{1,2,3}}
   {{2},{1,2}}
   {{1},{1},{1}}
4: {{1,2,3,4}}
   {{3},{1,2,3}}
   {{1,2},{1,2}}
   {{1,3},{2,3}}
   {{2},{2},{1,2}}
   {{1},{1},{1},{1}}
5: {{1,2,3,4,5}}
   {{4},{1,2,3,4}}
   {{1,4},{2,3,4}}
   {{2,3},{1,2,3}}
   {{2},{1,2},{1,2}}
   {{3},{3},{1,2,3}}
   {{3},{1,3},{2,3}}
   {{2},{2},{2},{1,2}}
   {{1},{1},{1},{1},{1}}

Crossrefs

Cf. A007716, A049311, A283877, A305854, A306006, A316980, A319616.

Cf. A319748, A319752, A319759, A319760, A319765, A319779, A319787, A319789.

Sequence in context: A011962 A060172 A193196 * A309807 A003243 A320160

Adjacent sequences: A319752 A319753 A319754 * A319756 A319757 A319758

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved