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A319642
Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of (not necessarily distinct) multisets.
0
1, 1, 2, 3, 6, 9, 16, 25, 42, 66, 108
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(5) = 9 antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1,2},{2,2}}
5: {{1,1,1,1,1}}
{{1,1,2,2,2}}
{{1,2,2,2,2}}
{{1,2,2,3,3}}
{{1,2,3,3,3}}
{{1,2,3,4,4}}
{{1,2,3,4,5}}
{{1,2},{2,2,2}}
{{3,3},{1,2,3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved