A319632 - OEIS

A319632

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

1, 1, 3, 5, 11, 17, 35, 53, 100, 154, 275

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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(4) = 11 set systems:

1: {{1}}

2: {{1,2}}

{{1},{1}}

{{1},{2}}

3: {{1,2,3}}

{{1},{2,3}}

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

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

{{1},{2},{3}}

4: {{1,2,3,4}}

{{1},{2,3,4}}

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

{{1,2},{3,4}}

{{1},{1},{2,3}}

{{1},{2},{3,4}}

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

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

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

{{1},{2},{3},{3}}

{{1},{2},{3},{4}}

CROSSREFS

Cf. A006126, A007716, A049311, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A147071 A006171 A261674 * A060647 A320353 A155989

Adjacent sequences: A319629 A319630 A319631 * A319633 A319634 A319635

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved