login
A319632
Number of non-isomorphic weight-n antichains of (not necessarily distinct) sets whose dual is also an antichain of (not necessarily distinct) sets.
0
1, 1, 3, 5, 11, 17, 35, 53, 100, 154, 275
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(4) = 11 set systems:
1: {{1}}
2: {{1,2}}
{{1},{1}}
{{1},{2}}
3: {{1,2,3}}
{{1},{2,3}}
{{1},{1},{1}}
{{1},{2},{2}}
{{1},{2},{3}}
4: {{1,2,3,4}}
{{1},{2,3,4}}
{{1,2},{1,2}}
{{1,2},{3,4}}
{{1},{1},{2,3}}
{{1},{2},{3,4}}
{{1},{1},{1},{1}}
{{1},{1},{2},{2}}
{{1},{2},{2},{2}}
{{1},{2},{3},{3}}
{{1},{2},{3},{4}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved