A319778 -id:A319778 - cp's OEIS frontend

A319792 Number of non-isomorphic connected set systems of weight n with empty intersection.

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

Gus Wiseman, Sep 27 2018

nonn

The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

			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}}

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A007716, A007718, A049311, A056156, A281116, A283877, A300913, A305854, A316980, A317752, A317755, A317757.

Cf. A319077, A319748, A319751, A319755, A319778, A319781, A319790.

a(n) = A300913(n) - A283877(n) + A319751(n). - Andrew Howroyd, May 31 2023

Terms a(11) and beyond from Andrew Howroyd, May 31 2023

A319793 Number of non-isomorphic connected strict multiset partitions (sets of multisets) of weight n with empty intersection.

Original entry on oeis.org

1, 0, 0, 0, 1, 4, 24, 96, 412, 1607, 6348, 24580, 96334, 378569, 1508220, 6079720, 24879878, 103335386, 436032901, 1869019800, 8139613977, 36008825317, 161794412893, 738167013847, 3418757243139, 16068569129711, 76622168743677, 370571105669576, 1817199912384794

Offset: 0

Gus Wiseman, Sep 27 2018

nonn

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

			Non-isomorphic representatives of the a(4) = 1 through a(5) = 4 multiset partitions:
4:  {{1},{2},{1,2}}
5: {{1},{2},{1,2,2}}
   {{1},{1,2},{2,2}}
   {{2},{3},{1,2,3}}
   {{2},{1,3},{2,3}}

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A007716, A007718, A056156, A281116, A283877, A316980, A317752, A317755, A317757, A319616.

Cf. A319077, A319748, A319755, A319778, A319781, A319791.

a(n) = A319557(n) - A316980(n) + A319077(n). - Andrew Howroyd, May 31 2023

Terms a(11) and beyond from Andrew Howroyd, May 31 2023

cp's OEIS Frontend

A319792 Number of non-isomorphic connected set systems of weight n with empty intersection.

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