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A369147
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Number of unlabeled loop-graphs covering n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).
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8
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0, 0, 1, 7, 52, 411, 4440, 73886, 2128608, 111533208, 10812478194, 1945437194308, 650378721118910, 404749938336301313, 470163239887698682289, 1022592854829028310302180, 4177826139658552046624979658, 32163829440870460348768017832607, 468021728889827507080865185809438918
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 0 through a(3) = 7 loop-graphs (loops shown as singletons):
. . {{1},{2},{1,2}} {{1},{2},{3},{1,2}}
{{1},{2},{1,2},{1,3}}
{{1},{2},{1,3},{2,3}}
{{1},{1,2},{1,3},{2,3}}
{{1},{2},{3},{1,2},{1,3}}
{{1},{2},{1,2},{1,3},{2,3}}
{{1},{2},{3},{1,2},{1,3},{2,3}}
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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], {1, 2}]], Union@@#==Range[n] && Length[Select[Tuples[#], UnsameQ@@#&]]==0&]]], {n, 0, 4}]
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CROSSREFS
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The complement for exactly n edges is A368984, labeled A333331 (maybe).
This is the covering case of A369146.
Cf. A000088, A000612, A005703, A055621, A062740, A134964, A137917, A140638, A367868, A368835, A369199.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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