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 A120414 Conjectured Ramsey number R(n,n). 1
 0, 1, 2, 6, 18, 45, 102, 213, 426, 821, 1538, 2820, 5075, 8996, 15743, 27247, 46709, 79405, 133996, 224640, 374400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS R(m,n) = minimal number of nodes R such that in any graph with R nodes there is either an m-clique or an independent set of size n. This sequence gives the diagonal entries R(n,n). Only these values have been proved: 0,1,2,6,18. a(5) is known to be in the range 43-49. - N. J. A. Sloane, Sep 16 2006 a(5) is at most 48, see the Angeltveit/McKay reference. - Jurjen N.E. Bos, Apr 11 2017 Ramsey numbers for simple binary partition. REFERENCES G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175. LINKS Vigleik Angeltveit, Brendan D. McKay, R(5,5) <= 48, arXiv:1703.08768 [math.CO], (Apr 10 2017). R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7. Eric Weisstein's World of Mathematics, Ramsey Number Wikipedia, Ramsey's Theorem. FORMULA a(n) = ceiling((3/2)^(n-3)*n*(n-1)), for n > 1. CROSSREFS Cf. A000791 (which has many more references). Sequence in context: A320303 A319415 A230137 * A251685 A341490 A308305 Adjacent sequences:  A120411 A120412 A120413 * A120415 A120416 A120417 KEYWORD easy,nonn AUTHOR Jeff Boscole (jazzerciser(AT)hotmail.com), Jul 06 2006 EXTENSIONS Edited by N. J. A. Sloane, Sep 16 2006 STATUS approved

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Last modified July 2 15:50 EDT 2022. Contains 355029 sequences. (Running on oeis4.)