A319565 Number of non-isomorphic connected strict T_0 multiset partitions of weight n.

1, 1, 1, 4, 8, 21, 62, 175, 553, 1775, 6007

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 A370956 A064503

Adjacent sequences: A319562 A319563 A319564 * A319566 A319567 A319568

Keyword

nonn,more

Author

Gus Wiseman, Sep 23 2018

Status

approved