

A330058


Number of nonisomorphic multiset partitions of weight n with at least one endpoint.


8



0, 1, 2, 7, 21, 68, 214, 706, 2335, 7968, 27661
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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.
An endpoint is a vertex appearing only once (degree 1).
Also the number of nonisomorphic multiset partitions of weight n with at least one singleton.


LINKS

Table of n, a(n) for n=0..10.
Wikipedia, Degree (graph theory)


EXAMPLE

Nonisomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions:
{1} {12} {122} {1222}
{1}{2} {123} {1233}
{1}{22} {1234}
{1}{23} {1}{222}
{2}{12} {12}{22}
{1}{2}{2} {1}{233}
{1}{2}{3} {12}{33}
{1}{234}
{12}{34}
{13}{23}
{2}{122}
{3}{123}
{1}{1}{23}
{1}{2}{22}
{1}{2}{33}
{1}{2}{34}
{1}{3}{23}
{2}{2}{12}
{1}{2}{2}{2}
{1}{2}{3}{3}
{1}{2}{3}{4}


CROSSREFS

The case of setsystems is A330053 (singletons) or A330052 (endpoints).
The complement is counted by A302545.
Cf. A007716, A283877, A306005, A330054, A330055, A330059.
Sequence in context: A126133 A186240 A274203 * A220726 A127540 A319852
Adjacent sequences: A330055 A330056 A330057 * A330059 A330060 A330061


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Nov 30 2019


STATUS

approved



