OFFSET
0,3
COMMENTS
The graphs considered here can have loops but not parallel edges.
Also the number of unlabeled loop-graphs with n edges and n vertices such that it is possible to choose a different vertex from each edge. - Gus Wiseman, Jan 25 2024
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
FORMULA
Euler transform of A368983.
EXAMPLE
Representatives of the a(3) = 5 graphs are:
{{1,2}, {1,3}, {2,3}},
{{1}, {1,2}, {1,3}},
{{1}, {1,2}, {2,3}},
{{1}, {2}, {2,3}},
{{1}, {2}, {3}}.
The graph with 4 vertices and edges {{1}, {2}, {1,2}, {3,4}} is included by A368599 but not by this sequence.
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}], {n}], Length[Select[Tuples[#], UnsameQ@@#&]]!=0&]]], {n, 0, 5}] (* Gus Wiseman, Jan 25 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 11 2024
STATUS
approved