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A369146
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Number of unlabeled loop-graphs with up to n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).
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13
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0, 0, 1, 8, 60, 471, 4911, 78797, 2207405, 113740613, 10926218807, 1956363413115, 652335084532025, 405402273420833338, 470568642161119515627, 1023063423471189429817807, 4178849203082023236054797465, 32168008290073542372004072630072, 468053896898117580623237189882068990
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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) = 8 loop-graphs (loops shown as singletons):
. . {{1},{2},{1,2}} {{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}]], Select[Tuples[#], UnsameQ@@#&]=={}&]]], {n, 0, 4}]
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CROSSREFS
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Without the choice condition we have A000666, labeled A006125 (shifted).
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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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