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A326871
Number of unlabeled connectedness systems covering n vertices.
7
1, 1, 4, 24, 436, 80460, 1689114556
OFFSET
0,3
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 any two overlapping edges. It is covering if every vertex belongs to some edge.
EXAMPLE
Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 connectedness systems:
{} {{1}} {{1,2}} {{1,2,3}}
{{1},{2}} {{1},{2,3}}
{{2},{1,2}} {{1},{2},{3}}
{{1},{2},{1,2}} {{3},{1,2,3}}
{{1},{3},{2,3}}
{{2,3},{1,2,3}}
{{2},{3},{1,2,3}}
{{1},{2,3},{1,2,3}}
{{1},{2},{3},{2,3}}
{{3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1},{3},{2,3},{1,2,3}}
{{2},{3},{2,3},{1,2,3}}
{{2},{1,3},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{2,3},{1,2,3}}
{{1},{2},{1,3},{2,3},{1,2,3}}
{{2},{3},{1,3},{2,3},{1,2,3}}
{{3},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,3},{2,3},{1,2,3}}
{{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
CROSSREFS
The non-covering case without singletons is A072444.
The case without singletons is A326899.
First differences of A326867 (the non-covering case).
Euler transform of A326869 (the connected case).
The labeled case is A326870.
Sequence in context: A167140 A010572 A247737 * A012945 A296398 A166947
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 29 2019
EXTENSIONS
a(5) from Andrew Howroyd, Aug 10 2019
a(6) from Andrew Howroyd, Oct 28 2023
STATUS
approved