A327228 Number of set-systems with n vertices and at least one endpoint/leaf.

0, 1, 6, 65, 3297, 2537672, 412184904221, 4132070624893905681577, 174224571863520492218909428465944685216436, 133392486801388257127953774730008469745829658368044283629394202488602260177922751

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

Andrew Howroyd, Table of n, a(n) for n = 0..12

Formula

Binomial transform of A327229.

a(n) = A058891(n+1) - A330059(n). - Andrew Howroyd, Jan 21 2023

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. A058891, A059167, A327098, A327103, A327104, A327107, A327197, A327227, A327230, A330059.

Sequence in context: A121017 A239998 A278841 * A359854 A284067 A137121

Adjacent sequences: A327225 A327226 A327227 * A327229 A327230 A327231

Keyword

nonn

Author

Gus Wiseman, Sep 01 2019

Extensions

Terms a(5) and beyond from Andrew Howroyd, Jan 21 2023

Status

approved