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, 2, 4, 6, 9, 12, 15, 18, 22, 26, 31, 35, 40

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

Table of n, a(n) for n=0..12.

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 A376343 A003066

Adjacent sequences: A157792 A157793 A157794 * A157796 A157797 A157798

Keyword

hard,more,nonn

Author

Terence Tao, Mar 07 2009

Status

approved