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A326866 Number of connectedness systems on n vertices. 26
1, 2, 8, 96, 6720, 8130432, 1100765114880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of two overlapping edges.

LINKS

Table of n, a(n) for n=0..6.

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

FORMULA

a(n) = 2^n * A072446(n).

EXAMPLE

The a(0) = 1 through a(2) = 8 connectedness systems:

  {}  {}     {}

      {{1}}  {{1}}

             {{2}}

             {{1,2}}

             {{1},{2}}

             {{1},{1,2}}

             {{2},{1,2}}

             {{1},{2},{1,2}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], SubsetQ[#, Union@@@Select[Tuples[#, 2], Intersection@@#!={}&]]&]], {n, 0, 3}]

CROSSREFS

The case without singletons is A072446.

The unlabeled case is A326867.

The connected case is A326868.

Binomial transform of A326870 (the covering case).

The BII-numbers of these set-systems are A326872.

Cf. A072444, A072447, A102896, A306445.

Sequence in context: A137704 A001417 A156926 * A001697 A006069 A270485

Adjacent sequences:  A326863 A326864 A326865 * A326867 A326868 A326869

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 29 2019

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)