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A319631 Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of distinct multisets. 0
1, 1, 2, 3, 5, 5, 13, 11, 25, 31, 54 (list; graph; refs; listen; history; text; internal format)
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(5) = 5 antichains:

1: {{1}}

2: {{1,1}}

   {{1},{1}}

3: {{1,1,1}}

   {{1,2,2}}

   {{1},{1},{1}}

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

   {{1,2,2,2}}

   {{1,1},{1,1}}

   {{1,2},{2,2}}

   {{1},{1},{1},{1}}

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

   {{1,1,2,2,2}}

   {{1,2,2,2,2}}

   {{1,2},{2,2,2}}

   {{1},{1},{1},{1},{1}}

CROSSREFS

Cf. A000219, A006126, A007716, A059201, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A156834 A079024 A342421 * A097453 A079125 A146305

Adjacent sequences:  A319628 A319629 A319630 * A319632 A319633 A319634

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified September 20 18:29 EDT 2021. Contains 347588 sequences. (Running on oeis4.)