

A330054


Number of nonisomorphic setsystems of weight n with no endpoints.


9



1, 0, 0, 0, 1, 0, 4, 4, 16, 26, 87
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,7


COMMENTS

A setsystem is a finite set of finite nonempty set of positive integers. An endpoint is a vertex appearing only once (degree 1). The weight of a setsystem 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.
Wikipedia, Degree (graph theory)


EXAMPLE

Nonisomorphic representatives of the a(0) = 1 through a(8) = 16 multiset partitions (empty columns not shown):
0 {1}{2}{12} {12}{13}{23} {13}{23}{123} {12}{134}{234}
{1}{23}{123} {1}{3}{23}{123} {1}{234}{1234}
{1}{2}{13}{23} {3}{12}{13}{23} {12}{34}{1234}
{1}{2}{3}{123} {1}{2}{3}{13}{23} {1}{12}{34}{234}
{12}{13}{24}{34}
{1}{2}{134}{234}
{1}{2}{34}{1234}
{2}{13}{14}{234}
{2}{13}{23}{123}
{3}{13}{23}{123}
{1}{2}{13}{24}{34}
{1}{2}{3}{14}{234}
{1}{2}{3}{23}{123}
{1}{2}{3}{4}{1234}
{2}{3}{12}{13}{23}
{1}{2}{3}{4}{12}{34}


CROSSREFS

The complement is counted by A330052.
The multiset partition version is A302545.
Nonisomorphic setsystems with no singletons are A306005.
Nonisomorphic setsystems counted by vertices are A000612.
Nonisomorphic setsystems counted by weight are A283877.
Cf. A007716, A055621, A317533, A317794, A319559, A320665, A330055, A330056, A330058.
Sequence in context: A053441 A065732 A092959 * A183433 A322039 A158101
Adjacent sequences: A330051 A330052 A330053 * A330055 A330056 A330057


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Nov 30 2019


STATUS

approved



