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A369202
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Number of unlabeled simple graphs covering n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).
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5
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0, 0, 0, 0, 2, 13, 95, 826, 11137, 261899, 11729360, 1006989636, 164072166301, 50336940172142, 29003653625802754, 31397431814146891910, 63969589218557753075156, 245871863137828405124380563, 1787331789281458167615190373076, 24636021675399858912682459601585276
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OFFSET
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0,5
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COMMENTS
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These are simple graphs covering n vertices such that some connected component has at least two cycles.
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LINKS
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FORMULA
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EXAMPLE
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Representatives of the a(4) = 2 and a(5) = 13 simple graphs:
{12}{13}{14}{23}{24} {12}{13}{14}{15}{23}{24}
{12}{13}{14}{23}{24}{34} {12}{13}{14}{15}{23}{45}
{12}{13}{14}{23}{24}{35}
{12}{13}{14}{23}{25}{45}
{12}{13}{14}{25}{35}{45}
{12}{13}{14}{15}{23}{24}{25}
{12}{13}{14}{15}{23}{24}{34}
{12}{13}{14}{15}{23}{24}{35}
{12}{13}{14}{23}{24}{35}{45}
{12}{13}{14}{15}{23}{24}{25}{34}
{12}{13}{14}{15}{23}{24}{35}{45}
{12}{13}{14}{15}{23}{24}{25}{34}{35}
{12}{13}{14}{15}{23}{24}{25}{34}{35}{45}
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MATHEMATICA
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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], {2}]], Union@@#==Range[n] && Length[Select[Tuples[#], UnsameQ@@#&]]==0&]]], {n, 0, 5}]
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CROSSREFS
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The complement is counted by A368834.
A005703 counts unlabeled connected choosable simple graphs, labeled A129271.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
Cf. A000088, A000612, A006649, A001434, A055621, A137916, A137917, A140638, A368596, A369141, A369146.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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