A199298 Number of nonseparable self-complementary graphs on n nodes.

0, 0, 0, 1, 0, 0, 9, 34, 0, 0, 710, 5564, 0, 0, 703040, 11214400, 0, 0, 9167628016, 293282496992, 0, 0, 1601362631008768, 102484554971313664, 0, 0, 3837877364995133299200, 491247174830495384679424, 0, 0, 128777253726458141919084341248, 32966970567472655355824573149184

Offset: 2

Author

N. J. A. Sloane, Nov 04 2011

Keywords

• nonn

Links

• Ken-ichi Kawarabayashi et al., On separable self-complementary graphs, Discrete Math., 257 (2002), 165-168.

Crossrefs

Cf. A000171.

Programs

Mathematica

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];
edges[v_] := 4 Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]}] + 2 Total[v];
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!]];
a[n_] := A000171[n] - A000171[n - 4];
Table[a[n], {n, 2, 33}] (* Jean-François Alcover, Aug 27 2019, after Andrew Howroyd *)

Formula

a(n) = A000171(n) - A000171(n-4) for n >= 4.

Extensions

Terms a(20) and beyond from Andrew Howroyd, Sep 17 2018