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
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