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A327229 Number of set-systems covering n vertices with at least one endpoint/leaf. 12
0, 1, 4, 50, 3069 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Covering means there are no isolated vertices.

A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. A leaf is an edge containing a vertex that does not belong to any other edge, while an endpoint is a vertex belonging to only one edge.

Also covering set-systems with minimum vertex-degree 1.

LINKS

Table of n, a(n) for n=0..4.

FORMULA

Inverse binomial transform of A327228.

EXAMPLE

The a(2) = 4 set-systems:

  {{1,2}}

  {{1},{2}}

  {{1},{1,2}}

  {{2},{1,2}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 3}]

CROSSREFS

The non-covering version is A327228.

The specialization to simple graphs is A327227.

The unlabeled version is A327230.

BII-numbers of these set-systems are A327105.

Cf. A003465, A245797, A327079, A327098, A327103, A327107, A327197.

Sequence in context: A201209 A026865 A016078 * A231832 A193157 A235604

Adjacent sequences:  A327226 A327227 A327228 * A327230 A327231 A327232

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 01 2019

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)