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A370316
Number of unlabeled simple graphs covering n vertices with at most n edges.
6
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
OFFSET
0,4
LINKS
EXAMPLE
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}
MATHEMATICA
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}]
PROG
(PARI) \\ G defined in A008406.
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
CROSSREFS
The connected case is A005703, labeled A129271.
The case of exactly n edges is A006649, covering case of A001434.
The labeled version is A369191.
Partial row sums of A370167, covering case of A008406.
The non-covering version with loops is A370168, labeled A066383.
The version with loops is A370169, labeled A369194.
The non-covering version is A370315, labeled A369192.
A006125 counts graphs, unlabeled A000088.
A006129 counts covering graphs, unlabeled A002494.
A322661 counts covering loop-graphs, unlabeled A322700.
Sequence in context: A120896 A074801 A324838 * A257889 A363388 A287963
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 18 2024
EXTENSIONS
a(8) onwards from Andrew Howroyd, Feb 19 2024
STATUS
approved