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A318099 Number of non-isomorphic weight-n antichains of (not necessarily distinct) multisets whose dual is also an antichain of (not necessarily distinct) multisets. 32
1, 1, 4, 7, 19, 32, 81, 142, 337, 659, 1564 (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(3) = 7 antichains:

1: {{1}}

2: {{1,1}}

   {{1,2}}

   {{1},{1}}

   {{1},{2}}

3: {{1,1,1}}

   {{1,2,3}}

   {{1},{2,2}}

   {{1},{2,3}}

   {{1},{1},{1}}

   {{1},{2},{2}}

   {{1},{2},{3}}

CROSSREFS

Cf. A000219, A006126, A007716, A049311, A059201, A283877, A306007, A316980, A316983, A319558, A319560, A319616-A319646, A300913.

Sequence in context: A164265 A174465 A006381 * A274691 A102991 A298350

Adjacent sequences:  A318096 A318097 A318098 * A318100 A318101 A318102

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)