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A157795
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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. triplets (a+r,b,c), (a,b+r,c), (a,b,c+r) with r positive
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0
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1, 2, 4, 6, 9, 12, 15, 18, 22, 26, 31, 35, 40
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..12.
Polymath1 wiki page for this sequence
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EXAMPLE
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For n=2, a four-point set without triangles is (2,0,0), (0,0,2), (1,1,0), (0,1,1).
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CROSSREFS
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Sequence in context: A083652 A118103 A185601 * A003066 A075349 A156024
Adjacent sequences: A157792 A157793 A157794 * A157796 A157797 A157798
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KEYWORD
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hard,more,nonn
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AUTHOR
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Terence Tao, Mar 07 2009
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STATUS
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approved
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