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A157795 Largest subset of the discrete triangular grid { (a,b,c): a+b+c = n, a,b,c >= 0 } that does not contain any upward-pointing triangles (i.e., triples (a+r,b,c), (a,b+r,c), (a,b,c+r) with r positive). 1
1, 2, 4, 6, 9, 12, 15, 18, 22, 26, 31, 35, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The n=3 case was posed as a problem by Fujimura. The sequence is related to a certain "hyper-optimistic conjecture" regarding the density Hales-Jewett theorem.
LINKS
Polymath1 wiki, Fujimura's problem
EXAMPLE
For n=2, a four-point set without triangles is (2,0,0), (0,0,2), (1,1,0), (0,1,1).
CROSSREFS
Sequence in context: A118103 A337134 A185601 * A294060 A003066 A075349
KEYWORD
hard,more,nonn
AUTHOR
Terence Tao, Mar 07 2009
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)