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A372172
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Number of labeled simple graphs on n vertices with exactly one triangle.
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14
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0, 0, 0, 1, 16, 290, 6980, 235270, 11298056, 777154308, 76560083040
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history;
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OFFSET
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0,5
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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) = 16 graphs:
12,13,23
12,14,24
13,14,34
23,24,34
12,13,14,23
12,13,14,24
12,13,14,34
12,13,23,24
12,13,23,34
12,14,23,24
12,14,24,34
12,23,24,34
13,14,23,34
13,14,24,34
13,23,24,34
14,23,24,34
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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}]], Length[cys[#]]==1&]], {n, 0, 5}]
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CROSSREFS
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For all cycles (not just triangles) we have A372193, covering A372195.
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KEYWORD
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nonn,more,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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