login
This site is supported by donations to The OEIS Foundation.
Logo

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. The next terms is known to be in the range 43-49. - N. J. A. Sloane, Sep 16 2006

Ramsey numbers for simple binary partition.

REFERENCES

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

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

LINKS

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

Eric Weisstein's World of Mathematics, Ramsey Number

Wikipedia, Ramsey's Theorem.

FORMULA

a(n) = ceil((3/2)^(n-3)*n*(n-1))

CROSSREFS

Cf. A000791 (which has many more references).

Sequence in context: A195584 A225316 A192708 * A054136 A140960 A072827

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 21 12:55 EDT 2013. Contains 225488 sequences.