

A006785


Number of trianglefree graphs on n vertices.
(Formerly M0841)


18



1, 2, 3, 7, 14, 38, 107, 410, 1897, 12172, 105071, 1262180, 20797002, 467871369, 14232552452, 581460254001, 31720840164950
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OFFSET

1,2


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..17.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
CombOS  Combinatorial Object Server, generate graphs
P. Erdős, D. J. Kleitman, and B. L. Rothschild, Asymptotic enumeration of k_nfree graphs. In Colloquio Internazionale sulle Teorie Combinatorie, (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 1927. Accad. Naz. Lincei, Rome.
Brendan McKay, Emails to N. J. A. Sloane, 1991
B. D. McKay, Isomorphfree exhaustive generation, J Algorithms, 26 (1998) 306324.
W. Pu, J. Choi, E. Amir, Lifted Inference On Transitive Relations, Workshops at the TwentySeventh AAAI Conference on Statistical Relational Artificial Intelligence, 2013.
Eric Weisstein's World of Mathematics, TriangleFree Graph


FORMULA

Erdős, Kleitman, & Rothschild prove that a(n) = 2^(n^2/4 + o(n^2)) and a(n) = (1 + o(1/n))*A033995(n).  Charles R Greathouse IV, Feb 01 2018


CROSSREFS

Cf. A024607.
Row sums of A283417.
Sequence in context: A089790 A296417 A296418 * A274538 A113182 A165433
Adjacent sequences: A006782 A006783 A006784 * A006786 A006787 A006788


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

2 more terms (from the McKay paper) from Vladeta Jovovic, May 17 2008
2 more terms from Brendan McKay, Jan 12 2013


STATUS

approved



