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A320798
Number of non-isomorphic weight-n connected antichains of non-constant multisets with multiset density -1.
7
0, 1, 2, 5, 9, 24, 51, 134, 328, 868
OFFSET
1,3
COMMENTS
The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.
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(2) = 1 through a(6) = 24 multiset partitions:
{{12}} {{122}} {{1122}} {{11222}} {{111222}}
{{123}} {{1222}} {{12222}} {{112222}}
{{1233}} {{12233}} {{112233}}
{{1234}} {{12333}} {{122222}}
{{13}{23}} {{12344}} {{122333}}
{{12345}} {{123333}}
{{12}{233}} {{123344}}
{{13}{233}} {{123444}}
{{14}{234}} {{123455}}
{{123456}}
{{112}{233}}
{{122}{233}}
{{12}{2333}}
{{123}{344}}
{{124}{344}}
{{125}{345}}
{{13}{2233}}
{{13}{2333}}
{{13}{2344}}
{{133}{233}}
{{14}{2344}}
{{15}{2345}}
{{13}{24}{34}}
{{14}{24}{34}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 29 2018
STATUS
approved