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A054915 Number of unlabeled connected graphs with n nodes such that complement is also connected. 1

%I

%S 1,0,0,1,8,68,662,9888,247492,11427974,994403266,163028488360,

%T 50169784370486,28952819268460634,31368276315718175152,

%U 63938104521922794457626,245807799210635120355337360,1787085725352186477232522962312,24634233605674730786262294027930520

%N Number of unlabeled connected graphs with n nodes such that complement is also connected.

%H Andrew Howroyd, <a href="/A054915/b054915.txt">Table of n, a(n) for n = 1..50</a>

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = 2*A001349(n) - A000088(n).

%t nn = 15; Clear[g, c, a, b]; c[z_] := Sum[a[n] z^n, {n, 1, nn}];

%t g[z_] := Sum[NumberOfGraphs[n] z^n, {n, 0, nn}]; sol =

%t SolveAlways[ 0 == Series[g[z] - Product[1/(1 - z^i)^a[i], {i, 1, nn}], {z, 0, nn}], z]; 2*(Flatten[Table[a[n], {n, 1, nn}] /. sol]) - (Drop[

%t CoefficientList[Series[g[z], {z, 0, nn + 1}], z], 1]) (* _Geoffrey Critzer_, Aug 12 2016 *)

%Y Cf. A000088, A001349.

%K nonn,easy

%O 1,5

%A _N. J. A. Sloane_, May 23 2000

%E More terms from _Vladeta Jovovic_, Jul 17 2000

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Last modified May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)