OFFSET
0,4
COMMENTS
Unlike the connected case (A057500), these graphs may have more than one cycle; for example, the graph {{1,2},{1,3},{1,4},{2,3},{2,4},{5,6}} has multiple cycles.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
Binomial transform of A367863.
EXAMPLE
Non-isomorphic representatives of the a(4) = 20 graphs:
{}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,4},{2,3}}
{{1,2},{1,3},{2,4},{3,4}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[#]==Length[Union@@#]&]], {n, 0, 5}]
PROG
(PARI) \\ Here b(n) is A367863(n)
b(n) = sum(k=0, n, (-1)^(n-k) * binomial(n, k) * binomial(binomial(k, 2), n))
a(n) = sum(k=0, n, binomial(n, k) * b(k)) \\ Andrew Howroyd, Dec 29 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 07 2023
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Dec 29 2023
STATUS
approved