

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
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OFFSET

0,3


COMMENTS

R(m,n) = minimal number of nodes R such that in any graph with R nodes there is either an mclique 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 4349.  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), 17.
Eric Weisstein's World of Mathematics, Ramsey Number
Wikipedia, Ramsey's Theorem.


FORMULA

a(n) = ceiling((3/2)^(n3)*n*(n1)), 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



