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A319565 Number of non-isomorphic connected strict T_0 multiset partitions of weight n. 20
1, 1, 1, 4, 8, 21, 62, 175, 553, 1775, 6007 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. The T_0 condition means that there are no equivalent vertices.

The weight of a multiset partition 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(4) = 8 multiset partitions:

1:      {{1}}

2:     {{1,1}}

3:    {{1,1,1}}

      {{1,2,2}}

     {{1},{1,1}}

     {{2},{1,2}}

4:   {{1,1,1,1}}

     {{1,2,2,2}}

    {{1},{1,1,1}}

    {{1},{1,2,2}}

    {{2},{1,2,2}}

    {{1,2},{2,2}}

    {{1,3},{2,3}}

   {{1},{2},{1,2}}

CROSSREFS

Cf. A007716, A007718, A049311, A056156, A059201, A283877, A316980.

Cf. A319557, A319558, A319559, A319560, A319564, A319566, A319567.

Sequence in context: A097076 A003608 A248423 * A129794 A064503 A050482

Adjacent sequences:  A319562 A319563 A319564 * A319566 A319567 A319568

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 23 2018

STATUS

approved

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Last modified November 14 15:08 EST 2019. Contains 329126 sequences. (Running on oeis4.)