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A319645
Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of distinct multisets.
0
1, 1, 1, 2, 3, 4, 7, 9, 16, 22, 38
OFFSET
0,4
COMMENTS
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. 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(6) = 7 antichains:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
{{1,2,2}}
4: {{1,1,1,1}}
{{1,2,2,2}}
{{1,2},{2,2}}
5: {{1,1,1,1,1}}
{{1,1,2,2,2}}
{{1,2,2,2,2}}
{{1,2},{2,2,2}}
6: {{1,1,1,1,1,1}}
{{1,1,2,2,2,2}}
{{1,2,2,2,2,2}}
{{1,2,2,3,3,3}}
{{1,2},{2,2,2,2}}
{{1,2,2},{2,2,2}}
{{1,2,3},{2,3,3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved