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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

Table of n, a(n) for n=0..20.

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 June 21 09:45 EDT 2021. Contains 345358 sequences. (Running on oeis4.)