A319782 - OEIS

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

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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},{1,1}}

{{2},{1,2}}

4: {{1,1,1,1}}

{{1},{1,1,1}}

{{1},{1,2,2}}