OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
The a(0) = 1 through a(4) = 19 loop-graph edge sets (loops shown as singletons):
{} {{1}} {{1,2}} {{1},{2,3}} {{1,2},{3,4}}
{{1},{2}} {{1,2},{1,3}} {{1},{2},{3,4}}
{{1},{1,2}} {{1},{2},{3}} {{1},{1,2},{3,4}}
{{1},{2},{1,3}} {{1},{2,3},{2,4}}
{{1},{1,2},{1,3}} {{1},{2},{3},{4}}
{{1},{1,2},{2,3}} {{1,2},{1,3},{1,4}}
{{1,2},{1,3},{2,3}} {{1,2},{1,3},{2,4}}
{{1},{2},{3},{1,4}}
{{1},{2},{1,2},{3,4}}
{{1},{2},{1,3},{1,4}}
{{1},{2},{1,3},{2,4}}
{{1},{2},{1,3},{3,4}}
{{1},{1,2},{1,3},{1,4}}
{{1},{1,2},{1,3},{2,4}}
{{1},{1,2},{2,3},{2,4}}
{{1},{1,2},{2,3},{3,4}}
{{1},{2,3},{2,4},{3,4}}
{{1,2},{1,3},{1,4},{2,3}}
{{1,2},{1,3},{2,4},{3,4}}
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]&&Length[#]<=n&]]], {n, 0, 5}]
PROG
(PARI) \\ G defined in A070166.
a(n)=my(A=O(x*x^n)); if(n==0, 1, polcoef((G(n, A)-G(n-1, A))/(1-x), n)) \\ Andrew Howroyd, Feb 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 16 2024
EXTENSIONS
a(7) onwards from Andrew Howroyd, Feb 19 2024
STATUS
approved