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A327228 Number of set-systems with n vertices and at least one endpoint/leaf. 8
0, 1, 6, 65, 3297 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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 set-systems with minimum covered vertex-degree 1.

LINKS

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

FORMULA

Binomial transform of A327229.

EXAMPLE

The a(2) = 6 set-systems:

  {{1}}

  {{2}}

  {{1,2}}

  {{1},{2}}

  {{1},{1,2}}

  {{2},{1,2}}

MATHEMATICA

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

CROSSREFS

The covering version is A327229.

The specialization to simple graphs is A245797.

BII-numbers of these set-systems are A327105.

Cf. A059167, A327098, A327103, A327104, A327107, A327197, A327227, A327230.

Sequence in context: A121017 A239998 A278841 * A284067 A137121 A110222

Adjacent sequences:  A327225 A327226 A327227 * A327229 A327230 A327231

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 01 2019

STATUS

approved

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Last modified February 23 07:11 EST 2020. Contains 332159 sequences. (Running on oeis4.)