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A006785 Number of triangle-free graphs on n vertices.
(Formerly M0841)
1, 2, 3, 7, 14, 38, 107, 410, 1897, 12172, 105071, 1262180, 20797002, 467871369, 14232552452, 581460254001, 31720840164950 (list; graph; refs; listen; history; text; internal format)



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


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_n-free graphs. In Colloquio Internazionale sulle Teorie Combinatorie, (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 19-27. Accad. Naz. Lincei, Rome.

Brendan McKay, Emails to N. J. A. Sloane, 1991

B. D. McKay, Isomorph-free exhaustive generation, J Algorithms, 26 (1998) 306-324.

W. Pu, J. Choi, E. Amir, Lifted Inference On Transitive Relations, Workshops at the Twenty-Seventh AAAI Conference on Statistical Relational Artificial Intelligence, 2013.

Eric Weisstein's World of Mathematics, Triangle-Free Graph


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


Cf. A024607.

Row sums of A283417.

Sequence in context: A089790 A296417 A296418 * A274538 A113182 A165433

Adjacent sequences:  A006782 A006783 A006784 * A006786 A006787 A006788




N. J. A. Sloane.


2 more terms (from the McKay paper) from Vladeta Jovovic, May 17 2008

2 more terms from Brendan McKay, Jan 12 2013



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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)