A319628 - OEIS

A319628

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

1, 1, 2, 2, 3, 3, 10, 11, 37, 80, 233

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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.

FORMULA

Euler transform is A319641.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(6) = 10 antichains:

1: {{1}}

2: {{1,1}}

3: {{1,1,1}}

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

5: {{1,1,1,1,1}}

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

6: {{1,1,1,1,1,1}}

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

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

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

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

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

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

CROSSREFS

Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646.

Sequence in context: A353563 A360250 A095060 * A094117 A097365 A156906

Adjacent sequences: A319625 A319626 A319627 * A319629 A319630 A319631

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved