A318099 - OEIS

A318099

Number of non-isomorphic weight-n antichains of (not necessarily distinct) multisets whose dual is also an antichain of (not necessarily distinct) multisets.

1, 1, 4, 7, 19, 32, 81, 142, 337, 659, 1564

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OFFSET

0,3

COMMENTS

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(3) = 7 antichains:

1: {{1}}

2: {{1,1}}

{{1},{1}}

{{1},{2}}

3: {{1,1,1}}

{{1},{2,2}}

{{1},{2,3}}