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A319719
Number of non-isomorphic connected antichains of multisets of weight n.
25
1, 1, 3, 4, 10, 14, 48, 95, 305, 822, 2615
OFFSET
0,3
COMMENTS
In an antichain, no part is a proper submultiset of any other. The weight of an antichain is the sum of sizes of its parts. Weight is generally not the same as number of vertices. Connected antichains are also called clutters.
LINKS
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 10 connected antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1,1},{1,1}}
{{1,2},{1,2}}
{{1,2},{2,2}}
{{1,3},{2,3}}
{{1},{1},{1},{1}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 26 2018
STATUS
approved