login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: A325544 A118103 A185601 * A294060 A003066 A075349

Adjacent sequences:  A157792 A157793 A157794 * A157796 A157797 A157798

KEYWORD

hard,more,nonn

AUTHOR

Terence Tao, Mar 07 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)