A003323 - OEIS

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A003323

Multicolor Ramsey numbers R(3,3,...,3).
(Formerly M2594)

3, 6, 17, 66, 327 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`A073591(n) is an upper bound on a(n).` `If the edges of a complete graph with at least as many nodes as a(n) are colored with n colors then there is always a monochromatic triangle.`
	REFERENCES	`G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175.` `H. W. Gould, personal communication.` `R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7.` `N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).`
	EXAMPLE	`a(2)=6 since in a party with at least 6 people, there are three people mutually acquainted or three people mutually unacquainted.`
	CROSSREFS	`Cf. A045652.` `Sequence in context: A143093 A117712 A106158 * A073591 A195995 A078318` `Adjacent sequences: A003320 A003321 A003322 * A003324 A003325 A003326`
	KEYWORD	`nonn`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com).`
	EXTENSIONS	`Upper bound and additional comments from D. G. Rogers (drogers(AT)turing.une.edu.au), Aug 27 2006` `Better definition from Max Alekseyev, Jan 12 2008` `Comment corrected by Brian Kell (bkell(AT)cmu.edu), Feb 14 2010`

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.