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

0,6

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

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

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}}

Crossrefs

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

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

Sequence in context: A023625 A166754 A026589 * A091002 A330419 A025176

Adjacent sequences: A319789 A319790 A319791 * A319793 A319794 A319795

Keyword

nonn

Author

Gus Wiseman, Sep 27 2018

Extensions

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

Status

approved