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A319566 Number of non-isomorphic connected T_0 set systems of weight n. 7
1, 1, 0, 1, 2, 3, 8, 17, 41, 103, 276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

In a set system, two vertices are equivalent if in every block the presence of the first is equivalent to the presence of the second. The T_0 condition means that there are no equivalent vertices.

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

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(6) = 8 set systems:

1:        {{1}}

3:     {{2},{1,2}}

4:    {{1,3},{2,3}}

     {{1},{2},{1,2}}

5:  {{2},{3},{1,2,3}}

    {{2},{1,3},{2,3}}

    {{3},{1,3},{2,3}}

6: {{3},{1,4},{2,3,4}}

   {{3},{2,3},{1,2,3}}

   {{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, A007718, A049311, A056156, A059201, A283877, A316980.

Cf. A319557, A319558, A319559, A319560, A319564, A319565, A319567.

Sequence in context: A298405 A219788 A099965 * A294450 A292852 A148014

Adjacent sequences:  A319563 A319564 A319565 * A319567 A319568 A319569

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 23 2018

STATUS

approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)