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A372168
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Number of triangle-free simple labeled graphs covering n vertices.
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14
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1, 0, 1, 3, 22, 237, 3961, 99900, 3757153, 208571691, 16945953790, 1999844518737, 340422874696873, 83041703920313712, 28850117307732482737, 14191512425207950473867, 9829313296102303971441502
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 22 graphs are:
12-34
13-24
14-23
12-13-14
12-13-24
12-13-34
12-14-23
12-14-34
12-23-24
12-23-34
12-24-34
13-14-23
13-14-24
13-23-24
13-23-34
13-24-34
14-23-24
14-23-34
14-24-34
12-13-24-34
12-14-23-34
13-14-23-24
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MATHEMATICA
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cys[y_]:=Select[Subsets[Union@@y, {3}], MemberQ[y, {#[[1]], #[[2]]}] && MemberQ[y, {#[[1]], #[[3]]}] && MemberQ[y, {#[[2]], #[[3]]}]&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[cys[#]]==0&]], {n, 0, 5}]
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CROSSREFS
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For all cycles (not just triangles) we have A105784, unlabeled A144958.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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