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A319557 Number of non-isomorphic strict connected multiset partitions of weight n. 25
1, 1, 2, 5, 12, 30, 91, 256, 823, 2656, 9103 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Also the number of non-isomorphic connected T_0 multiset partitions of weight n. 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.

LINKS

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

FORMULA

Inverse Euler transform of A316980.

EXAMPLE

Non-isomorphic representatives of the a(4) = 12 strict connected multiset partitions:

    {{1,1,1,1}}

    {{1,1,2,2}}

    {{1,2,2,2}}

    {{1,2,3,3}}

    {{1,2,3,4}}

   {{1},{1,1,1}}

   {{1},{1,2,2}}

   {{2},{1,2,2}}

   {{3},{1,2,3}}

   {{1,2},{2,2}}

   {{1,3},{2,3}}

  {{1},{2},{1,2}}

Non-isomorphic representatives of the a(4) = 12 connected T_0 multiset partitions:

     {{1,1,1,1}}

     {{1,2,2,2}}

    {{1},{1,1,1}}

    {{1},{1,2,2}}

    {{2},{1,2,2}}

    {{1,1},{1,1}}

    {{1,2},{2,2}}

    {{1,3},{2,3}}

   {{1},{1},{1,1}}

   {{1},{2},{1,2}}

   {{2},{2},{1,2}}

  {{1},{1},{1},{1}}

CROSSREFS

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

Cf. A319558, A319559, A319560, A319564, A319565, A319566, A319567.

Sequence in context: A261788 A112412 A309506 * A261937 A305311 A291239

Adjacent sequences:  A319554 A319555 A319556 * A319558 A319559 A319560

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 23 2018

STATUS

approved

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Last modified May 12 06:54 EDT 2021. Contains 343820 sequences. (Running on oeis4.)