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A319792
Number of non-isomorphic connected set systems of weight n with empty intersection.
1
1, 0, 0, 0, 1, 2, 9, 22, 69, 190, 567, 1640, 5025, 15404, 49048, 159074, 531165, 1813627, 6352739, 22759620, 83443086, 312612543, 1196356133, 4672620842, 18615188819, 75593464871, 312729620542, 1317267618429, 5646454341658, 24618309943464, 109123789229297
OFFSET
0,6
COMMENTS
The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
LINKS
FORMULA
a(n) = A300913(n) - A283877(n) + A319751(n). - Andrew Howroyd, May 31 2023
EXAMPLE
Non-isomorphic representatives of the a(4) = 1 through a(6) = 9 connected set systems:
4: {{1},{2},{1,2}}
5: {{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
6: {{1},{1,4},{2,3,4}}
{{1},{2,3},{1,2,3}}
{{3},{4},{1,2,3,4}}
{{3},{1,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,3},{2,3}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 27 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, May 31 2023
STATUS
approved