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A000791 Ramsey numbers R(3,n).
(Formerly M2530 N0998)
3, 6, 9, 14, 18, 23, 28, 36 (list; graph; refs; listen; history; text; internal format)



The next term is known to be 40, 41, 42 or 43 (Exoo, Radziszowski). I had a note here saying that the range had been narrowed to 40 or 41, but I cannot find the source for that remark, so I am not sure it is correct. - N. J. A. Sloane, Feb 14 2007

a(10) is either 40, 41, or 42 (Goedgebeur, Radziszowski). - Ray G. Opao, Oct 07 2015


G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 288.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 840.

Brendan McKay, personal communication.

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 42.

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).


Table of n, a(n) for n=2..9.

Anonymous, Ramsey's Theory [broken link?]

G. Exoo, Ramsey Numbers

R. Getschmann, Enumeration of Small Ramsey Graphs

J. Goedgebeur and S. Radziszowski, New Computational Upper Bounds for Ramsey Numbers R(3,k), arXiv:1210.5826 [math.CO], 2012-2013.

R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7.

J. G. Kalbfleisch, Construction of special edge-chromatic graphs, Canad. Math. Bull., 8 (1965), 575-584.

Richard L. Kramer, Ricardo's Ramsey Number Page

I. Leader, Friends and Strangers

Math Reference Project, Ramsey Numbers

B. McKay, Email to N. J. A. Sloane, Jul. 1991

Online Dictionary of Combinatorics, Ramsey's Theorem

I. Peterson, Math Trek, Party Games, Science News Online, Vol. 156,  No. 23,  December 4, 1999.

I. Peterson, Math Trek, Party Games, December 6, 1999.

Stanislaw Radziszowski, Small Ramsey Numbers, The Electronic Journal of Combinatorics, Dynamic Surveys, #DS1: Jan 12, 2014.

Eric Weisstein's World of Mathematics, Ramsey Number

Wikipedia, Ramsey's Theorem.

Jin Xu and C. K. Wong, Self-complementary graphs and Ramsey numbers I, Discrete Math., 223 (2000), 309-326.


A row of the table in A059442. Cf. A120414.

Sequence in context: A265321 A187263 A230876 * A027424 A294476 A258087

Adjacent sequences:  A000788 A000789 A000790 * A000792 A000793 A000794




N. J. A. Sloane



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Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)