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A319620 Number of connected antichain covers of n vertices by distinct sets whose dual is also a (not necessarily strict) antichain. 0
1, 1, 1, 2, 22, 2133 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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}}.

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

The a(4) = 22 antichain covers:

   {{1,2,3,4}}

   {{3,4},{1,2,3},{1,2,4}}

   {{2,4},{1,2,3},{1,3,4}}

   {{2,3},{1,2,4},{1,3,4}}

   {{1,4},{1,2,3},{2,3,4}}

   {{1,3},{1,2,4},{2,3,4}}

   {{1,2},{1,3,4},{2,3,4}}

   {{1,3},{1,4},{2,3},{2,4}}

   {{1,2},{1,4},{2,3},{3,4}}

   {{1,2},{1,3},{2,4},{3,4}}

   {{1,4},{2,4},{3,4},{1,2,3}}

   {{1,3},{2,3},{3,4},{1,2,4}}

   {{1,2},{2,3},{2,4},{1,3,4}}

   {{1,2},{1,3},{1,4},{2,3,4}}

   {{1,3},{1,4},{2,3},{2,4},{3,4}}

   {{1,2},{1,4},{2,3},{2,4},{3,4}}

   {{1,2},{1,3},{2,3},{2,4},{3,4}}

   {{1,2},{1,3},{1,4},{2,4},{3,4}}

   {{1,2},{1,3},{1,4},{2,3},{3,4}}

   {{1,2},{1,3},{1,4},{2,3},{2,4}}

   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

CROSSREFS

Cf. A006126, A007716, A007718, A049311, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

Sequence in context: A330124 A104149 A113761 * A054349 A182293 A222000

Adjacent sequences:  A319617 A319618 A319619 * A319621 A319622 A319623

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)