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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
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.
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}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved