|
| |
|
|
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
|
| |
|
|
