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A319625 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets. 1
1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

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 A319638.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(10) = 3 antichains:

               {{1}}

        {{1,2},{1,3},{2,3}}

     {{1,2},{1,3},{2,4},{3,4}}

    {{1,2},{1,3},{1,4},{2,3,4}}

   {{1,3},{2,4},{1,2,5},{3,4,5}}

  {{1,2},{1,3},{2,4},{3,5},{4,5}}

  {{1,3},{1,4},{2,3},{2,4},{3,4}}

CROSSREFS

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

Sequence in context: A257228 A160540 A186718 * A307802 A169585 A045840

Adjacent sequences:  A319622 A319623 A319624 * A319626 A319627 A319628

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)