

A330057


Number of setsystems covering n vertices with no singletons or endpoints.


3




OFFSET

0,4


COMMENTS

A setsystem is a finite set of finite nonempty set of positive integers. A singleton is an edge of size 1. An endpoint is a vertex appearing only once (degree 1).


LINKS

Table of n, a(n) for n=0..4.
Wikipedia, Degree (graph theory)


FORMULA

Binomial transform is A330056.


EXAMPLE

The a(3) = 5 setsystems:
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2, n}]], Union@@#==Range[n]&&Min@@Length/@Split[Sort[Join@@#]]>1&]], {n, 0, 4}]


CROSSREFS

The version for nonisomorphic setsystems is A330055 (by weight).
The noncovering version is A330056.
Setsystems with no singletons are A016031.
Setsystems with no endpoints are A330059.
Nonisomorphic setsystems with no singletons are A306005 (by weight).
Nonisomorphic setsystems with no endpoints are A330054 (by weight).
Nonisomorphic setsystems counted by vertices are A000612.
Nonisomorphic setsystems counted by weight are A283877.
Cf. A007716, A055621, A302545, A317533, A317794, A319559, A320665, A321405, A330052, A330058.
Sequence in context: A198246 A122465 A203683 * A324265 A003733 A201300
Adjacent sequences: A330054 A330055 A330056 * A330058 A330059 A330060


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Nov 30 2019


STATUS

approved



