cp's OEIS Frontend

A370315 Number of unlabeled simple graphs with n possibly isolated vertices and up to n edges.

%I A370315 #10 Feb 20 2024 19:28:41
%S A370315 1,1,2,4,9,20,54,146,436,1372,4577,15971,58376,221876,876012,3583099,
%T A370315 15159817,66248609,298678064,1387677971,6637246978,32648574416,
%U A370315 165002122350,855937433641,4553114299140,24813471826280,138417885372373,789683693019999,4603838061688077
%N A370315 Number of unlabeled simple graphs with n possibly isolated vertices and up to n edges.
%H A370315 Andrew Howroyd, <a href="/A370315/b370315.txt">Table of n, a(n) for n = 0..50</a>
%F A370315 Sum of first n+1 terms of row n of A008406.
%e A370315 The a(1) = 1 through a(4) = 9 graph edge sets:
%e A370315   {}  {}    {}          {}
%e A370315       {12}  {12}        {12}
%e A370315             {12-13}     {12-13}
%e A370315             {12-13-23}  {12-34}
%e A370315                         {12-13-14}
%e A370315                         {12-13-23}
%e A370315                         {12-13-24}
%e A370315                         {12-13-14-23}
%e A370315                         {12-13-24-34}
%t A370315 brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]],p[[i]]}, {i,Length[p]}])], {p,Permutations[Range[Length[Union@@m]]]}]]];
%t A370315 Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n],{2}]], Length[#]<=n&]]],{n,0,5}]
%o A370315 (PARI) a(n) = if(n<=1, n>=0, polcoef(G(n, O(x*x^n))/(1-x),n)) \\ G(n) defined in A008406. - _Andrew Howroyd_, Feb 20 2024
%Y A370315 The case of exactly n edges is A001434, covering A006649.
%Y A370315 The connected covering case is A005703, labeled A129271.
%Y A370315 Partial row sums of A008406, covering A370167.
%Y A370315 The labeled version is A369192.
%Y A370315 The version with loops is A370168, labeled A066383.
%Y A370315 The covering case is A370316, labeled A369191.
%Y A370315 A006125 counts graphs, unlabeled A000088.
%Y A370315 A006129 counts covering graphs, unlabeled A002494.
%Y A370315 Cf. A000666, A322661, A322700, A369194, A369196, A369197, A369199, A370169.
%K A370315 nonn
%O A370315 0,3
%A A370315 _Gus Wiseman_, Feb 18 2024