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A370168
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Number of unlabeled loop-graphs with n vertices and at most n edges.
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6
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1, 2, 5, 13, 36, 102, 313, 994, 3318, 11536, 41748, 156735, 609973, 2456235, 10224216, 43946245, 194866898, 890575047, 4190997666, 20289434813, 100952490046, 515758568587, 2703023502100, 14518677321040, 79852871813827, 449333028779385, 2584677513933282
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OFFSET
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0,2
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LINKS
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EXAMPLE
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The a(0) = 1 through a(3) = 13 loop-graph edge sets (loops shown as singletons):
{} {} {} {}
{{1}} {{1}} {{1}}
{{1,2}} {{1,2}}
{{1},{2}} {{1},{2}}
{{1},{1,2}} {{1},{1,2}}
{{1},{2,3}}
{{1,2},{1,3}}
{{1},{2},{3}}
{{1},{2},{1,2}}
{{1},{2},{1,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{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}]], Length[#]<=n&]]], {n, 0, 5}]
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PROG
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(PARI) a(n)=my(A=O(x*x^n)); if(n==0, 1, polcoef(G(n, A)/(1-x), n)) \\ G defined in A070166. - Andrew Howroyd, Feb 19 2024
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CROSSREFS
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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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