A319782 Number of non-isomorphic intersecting strict T_0 multiset partitions of weight n.

1, 1, 1, 4, 7, 17, 42, 98, 248, 631, 1657

Offset

0,4

Comments

A multiset partition is intersecting iff no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. 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 T_0 condition means the dual is strict.

Links

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

Example

Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 multiset partitions:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
   {{1,2,2}}
   {{1},{1,1}}
   {{2},{1,2}}
4: {{1,1,1,1}}
   {{1,2,2,2}}
   {{1},{1,1,1}}
   {{1},{1,2,2}}
   {{2},{1,2,2}}
   {{1,2},{2,2}}
   {{1,3},{2,3}}

Crossrefs

Cf. A007716, A049311, A059201, A281116, A283877, A305843, A305854, A306006, A316980.

Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319789.

Sequence in context: A009881 A049944 A098091 * A057450 A077274 A292850

Adjacent sequences: A319779 A319780 A319781 * A319783 A319784 A319785

Keyword

nonn,more

Author

Gus Wiseman, Sep 27 2018

Status

approved