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A005346 Van der Waerden numbers W(2,n).
(Formerly M2819)
9
1, 3, 9, 35, 178, 1132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Extension (2,6) found by researcher in SAT techniques. - Jonathan Braunhut (jonbraunhut(AT)gmail.com), Jul 29 2007

REFERENCES

J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 159.

M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 49.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..6.

P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics, L'Enseignement Math., Geneva, 1979, p. 325.

P. R. Herwig, M. J. H. Heule, P. M. van Lambalgen, H. van Maaren, A new method to construct lower bounds for Van de Waerden Numbers, Elec. J. Combinat. 14 (1) (2007), #R6.

M. Kouril and Jerome L. Paul, The van der Waerden Number W(2,6) Is 1132, Experimental Mathematics, 17 (2008), 53-61.

Eric Weisstein's World of Mathematics, van der Waerden Number

Wikipedia, Van der Waerden number.

CROSSREFS

Cf. A121894.

Sequence in context: A107894 A155858 A000834 * A129094 A059424 A002575

Adjacent sequences:  A005343 A005344 A005345 * A005347 A005348 A005349

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(6) from Jonathan Braunhut (jonbraunhut(AT)gmail.com), Jul 29 2007

STATUS

approved

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Last modified May 17 18:44 EDT 2021. Contains 343987 sequences. (Running on oeis4.)