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A319623 Number of connected antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets. 0
1, 1, 0, 1, 15, 1957 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichain covers:

1: {{1}}

3: {{1,2},{1,3},{2,3}}

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

   {{1,3},{1,4},{2,3},{2,4}}

   {{1,2},{1,4},{2,3},{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, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646, A300913.

Sequence in context: A110103 A232305 A282946 * A208875 A199098 A208784

Adjacent sequences:  A319620 A319621 A319622 * A319624 A319625 A319626

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 25 2018

STATUS

approved

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Last modified April 12 18:52 EDT 2021. Contains 342931 sequences. (Running on oeis4.)