OFFSET
0,3
FORMULA
First differences of A339832 (the non-covering version).
EXAMPLE
Representatives of the a(0) = 1 through a(3) = 9 loop-graphs (loops shown as singletons):
{} {{1}} {{1,2}} {{1},{2,3}}
{{1},{2}} {{1,2},{1,3}}
{{1},{1,2}} {{1},{2},{3}}
{{1},{2},{1,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{2,3}}
{{1,2},{1,3},{2,3}}
{{1},{2},{1,3},{2,3}}
{{1},{1,2},{1,3},{2,3}}
MATHEMATICA
brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n], {1, 2}]], Union@@#==Range[n] && !MatchQ[#, {___, {x_}, ___, {y_}, ___, {x_, y_}, ___}]&]]], {n, 0, 4}]
CROSSREFS
The non-covering version is A339832.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 12 2024
STATUS
approved