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A370316
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Number of unlabeled simple graphs covering n vertices with at most n edges.
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6
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1, 0, 1, 2, 5, 10, 28, 68, 193, 534, 1568, 4635, 14146, 43610, 137015, 435227, 1400058, 4547768, 14917504, 49348612, 164596939, 553177992, 1872805144, 6385039022, 21917878860, 75739158828, 263438869515, 922219844982, 3249042441125, 11519128834499, 41097058489426
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(0) = 1 through a(5) = 10 simple graphs:
{} . {12} {12-13} {12-34} {12-13-45}
{12-13-23} {12-13-14} {12-13-14-15}
{12-13-24} {12-13-14-25}
{12-13-14-23} {12-13-23-45}
{12-13-24-34} {12-13-24-35}
{12-13-14-15-23}
{12-13-14-23-25}
{12-13-14-23-45}
{12-13-14-25-35}
{12-13-24-35-45}
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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], {2}], {0, n}], Union@@#==Range[n]&]]], {n, 0, 5}]
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PROG
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a(n)=my(A=O(x*x^n)); if(n==0, 1, polcoef((G(n, A)-G(n-1, A))/(1-x), n)) \\ 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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