OFFSET
0,3
COMMENTS
From Gus Wiseman, Aug 01 2019: (Start)
If we define a connectedness system to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges, then a(n) is the number of unlabeled connectedness systems on n vertices without singleton edges. Non-isomorphic representatives of the a(3) = 6 connectedness systems without singletons are:
{}
{{1,2}}
{{1,2,3}}
{{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
(End)
LINKS
Wim van Dam, Sub Power Set Sequences
FORMULA
Euler transform of A072445. - Andrew Howroyd, Oct 28 2023
EXAMPLE
a(3) = 6 because of the 6 sets: {{1}, {2}, {3}}; {{1}, {2}, {3}, {1, 2}}; {{1}, {2}, {3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Wim van Dam (vandam(AT)cs.berkeley.edu), Jun 18 2002
EXTENSIONS
a(0)=1 prepended and a(6) corrected by Andrew Howroyd, Oct 28 2023
STATUS
approved