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A000171
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Number of self-complementary graphs with n nodes.
(Formerly M0014 N0780)
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9
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1, 0, 0, 1, 2, 0, 0, 10, 36, 0, 0, 720, 5600, 0, 0, 703760, 11220000, 0, 0, 9168331776, 293293716992, 0, 0, 1601371799340544, 102484848265030656, 0, 0, 3837878966366932639744, 491247277315343649710080, 0, 0
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OFFSET
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1,5
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COMMENTS
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a(n) = A007869(n)-A054960(n), where A007869(n) is number of unlabeled graphs with n nodes and an even number of edges and A054960(n) is number of unlabeled graphs with n nodes and an odd number of edges.
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REFERENCES
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Gibbs, Richard A. Self-complementary graphs. J. Combinatorial Theory Ser. B 16 (1974), 106--123. MR0347686 (50 #188). - N. J. A. Sloane, Mar 27 2012
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 139, Table 6.1.1.
R. C. Read, On the number of self-complementary graphs and digraphs, J. London Math. Soc., 38 (1963), 99-104.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wille, Enumeration of self-complementary structures, J. Comb. Theory B 25 (1978) 143-150.
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LINKS
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Table of n, a(n) for n=1..31.
H. Fripertinger, Self-complementary graphs
Eric Weisstein's World of Mathematics, Self-Complementary Graph
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FORMULA
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a(4n) = A003086(2n).
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MATHEMATICA
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<<Combinatorica`; Table[GraphPolynomial[n, x]/.x -> -1, {n, 1, 20}] (* Geoffrey Critzer, Oct 21 2012 *)
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CROSSREFS
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Cf. A047660, A051251, A047832.
Cf. A008406 (triangle of coefficients of the "graph polynomial").
Sequence in context: A010893 A181501 A213704 * A054922 A061848 A193294
Adjacent sequences: A000168 A000169 A000170 * A000172 A000173 A000174
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from R. C. Read (rcread(AT)math.uwaterloo.ca) and Vladeta Jovovic (vladeta(AT)eunet.rs).
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STATUS
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approved
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