

A157795


Largest subset of the discrete triangular grid { (a,b,c): a+b+c = n, a,b,c >= 0 } that does not contain any upwardpointing 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
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OFFSET

0,2


COMMENTS

The n=3 case was posed as a problem by Fujimura. The sequence is related to a certain "hyperoptimistic conjecture" regarding the density HalesJewett theorem.


LINKS

Table of n, a(n) for n=0..12.
Polymath1 wiki, Fujimura's problem


EXAMPLE

For n=2, a fourpoint 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
Adjacent sequences: A157792 A157793 A157794 * A157796 A157797 A157798


KEYWORD

hard,more,nonn


AUTHOR

Terence Tao, Mar 07 2009


STATUS

approved



