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A300913 Number of non-isomorphic connected set-systems of weight n. 26
1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.

LINKS

Table of n, a(n) for n=0..10.

FORMULA

Inverse Euler transform of A283877.

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:

1: {{1}}

2: {{1,2}}

3: {{1,2,3}}

   {{2},{1,2}}

4: {{1,2,3,4}}

   {{3},{1,2,3}}

   {{1,3},{2,3}}

   {{1},{2},{1,2}}

5: {{1,2,3,4,5}}

   {{4},{1,2,3,4}}

   {{1,4},{2,3,4}}

   {{2,3},{1,2,3}}

   {{2},{3},{1,2,3}}

   {{2},{1,3},{2,3}}

   {{3},{1,3},{2,3}}

Non-isomorphic representatives of the a(6) = 18 connected set-systems:

  {{1,2,3,4,5,6}}

  {{5},{1,2,3,4,5}}

  {{1,5},{2,3,4,5}}

  {{3,4},{1,2,3,4}}

  {{1,2,5},{3,4,5}}

  {{1,3,4},{2,3,4}}

  {{1},{1,4},{2,3,4}}

  {{1},{2,3},{1,2,3}}

  {{3},{4},{1,2,3,4}}

  {{3},{1,4},{2,3,4}}

  {{3},{2,3},{1,2,3}}

  {{4},{1,4},{2,3,4}}

  {{1,2},{1,3},{2,3}}

  {{1,3},{2,4},{3,4}}

  {{1,4},{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, A055621, A283877, A293606, A293607.

Sequence in context: A103032 A215649 A259351 * A232484 A223013 A276027

Adjacent sequences:  A300910 A300911 A300912 * A300914 A300915 A300916

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 19 2018

STATUS

approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)