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A319559 Number of non-isomorphic T_0 set systems of weight n. 40
1, 1, 1, 2, 4, 7, 16, 35, 82, 200, 517 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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(5) = 7 set systems:

1:        {{1}}

2:      {{1},{2}}

3:     {{2},{1,2}}

      {{1},{2},{3}}

4:    {{1,3},{2,3}}

     {{1},{2},{1,2}}

     {{1},{3},{2,3}}

    {{1},{2},{3},{4}}

5:  {{1},{2,4},{3,4}}

    {{2},{3},{1,2,3}}

    {{2},{1,3},{2,3}}

    {{3},{1,3},{2,3}}

   {{1},{2},{3},{2,3}}

   {{1},{2},{4},{3,4}}

  {{1},{2},{3},{4},{5}}

CROSSREFS

Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A305854, A306006, A316980, A317757.

Cf. A319557, A319558, A319560, A319564, A319565, A319566, A319567.

Sequence in context: A259544 A294376 A259545 * A260790 A151378 A192464

Adjacent sequences:  A319556 A319557 A319558 * A319560 A319561 A319562

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 23 2018

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)