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Search: id:A120414
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| A120414 |
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Conjectured Ramsey number R(n,n). |
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+0
2
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| 0, 1, 2, 6, 18, 45, 102, 213, 426, 821, 1538, 2820, 5075, 8996, 15743, 27247, 46709, 79405, 133996, 224640, 374400
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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 (njas(AT)research.att.com), Sep 16 2006
Ramsey numbers for simple binary partition.
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Ramsey Number
Wikipedia, Ramsey's Theorem.
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FORMULA
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a(n) = ceil((3/2)^(n-3)*n*(n-1))
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CROSSREFS
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Cf. A000791 (which has many more references).
Sequence in context: A014741 A016059 A027556 this_sequence A054136 A140960 A072827
Adjacent sequences: A120411 A120412 A120413 this_sequence A120415 A120416 A120417
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KEYWORD
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easy,nonn
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AUTHOR
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Jeff Boscole (jazzerciser(AT)hotmail.com), Jul 06 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 16 2006
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