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%I #13 Aug 27 2019 04:22:19
%S 0,0,0,1,0,0,9,34,0,0,710,5564,0,0,703040,11214400,0,0,9167628016,
%T 293282496992,0,0,1601362631008768,102484554971313664,0,0,
%U 3837877364995133299200,491247174830495384679424,0,0,128777253726458141919084341248,32966970567472655355824573149184
%N Number of nonseparable self-complementary graphs on n nodes.
%H Ken-ichi Kawarabayashi et al., <a href="https://doi.org/10.1016/S0012-365X(02)00399-0">On separable self-complementary graphs</a>, Discrete Math., 257 (2002), 165-168.
%F a(n) = A000171(n) - A000171(n-4) for n >= 4.
%t permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
%t edges[v_] := 4 Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]}] + 2 Total[v];
%t A000171[n_] := Module[{s = 0}, Switch[Mod[n, 4], 2 | 3, 0, _, Do[s += permcount[4 p]*2^edges[p]*If[OddQ[n], n*2^Length[p], 1], {p, IntegerPartitions[Quotient[n, 4]]}]; s/n!]];
%t a[n_] := A000171[n] - A000171[n - 4];
%t Table[a[n], {n, 2, 33}] (* _Jean-François Alcover_, Aug 27 2019, after _Andrew Howroyd_ *)
%Y Cf. A000171.
%K nonn
%O 2,7
%A _N. J. A. Sloane_, Nov 04 2011
%E Terms a(20) and beyond from _Andrew Howroyd_, Sep 17 2018
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