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A319618 Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of multisets. 0
1, 1, 3, 4, 9, 10, 24, 28, 57, 80, 138 (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(4) = 9 antichains:

1: {{1}}

2: {{1,1}}

   {{1,2}}

   {{1},{1}}

3: {{1,1,1}}

   {{1,2,2}}

   {{1,2,3}}

   {{1},{1},{1}}

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

   {{1,1,2,2}}

   {{1,2,2,2}}

   {{1,2,3,3}}

   {{1,2,3,4}}

   {{1,1},{1,1}}

   {{1,2},{1,2}}

   {{1,2},{2,2}}

   {{1},{1},{1},{1}}

CROSSREFS

Cf. A000219, A006126, A007716, A049311, A059201, A283877, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

Sequence in context: A277138 A327282 A126269 * A172980 A336930 A035252

Adjacent sequences:  A319615 A319616 A319617 * A319619 A319620 A319621

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified April 12 17:48 EDT 2021. Contains 342929 sequences. (Running on oeis4.)