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A319641 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets. 1
1, 1, 3, 5, 11, 18, 41, 70, 159, 323, 778 (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
FORMULA
Euler transform of A319628.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{2}}
3: {{1,1,1}}
{{1,2,3}}
{{1},{2,2}}
{{1},{2,3}}
{{1},{2},{3}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,3,4}}
{{1},{2,2,2}}
{{1},{2,3,4}}
{{1,1},{2,2}}
{{1,2},{3,3}}
{{1,2},{3,4}}
{{1},{2},{3,3}}
{{1},{2},{3,4}}
{{1},{2},{3},{4}}
CROSSREFS
Sequence in context: A269628 A162891 A320351 * A306895 A198519 A045957
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)