# [seqfan] Re: No right isosceles triangles in a square grid

Neil Sloane njasloane at gmail.com
Fri Apr 22 16:21:36 CEST 2016

```Giovanni, Thank you very much for those results!

They are now in A271906 and A271907

Sometime, could you add more illustrations for them? Perhaps like the
lovely pictures with red dots that you made for A227133?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Fri, Apr 22, 2016 at 9:10 AM, Giovanni Resta <g.resta at iit.cnr.it> wrote:

> On 04/22/2016 12:28 PM, Neil Sloane wrote:
>
> Take a square grid of n X n points. What is
>> the size of the largest subset S of these points
>> such that no three of the points of S form a right isosceles triangle?
>>
>> That is, S must not contain 3 points A,B,C such that angle ABC
>> = 90 degrees, and |AB| = |BC|.
>> I am pretty sure that a(1)=1, a(2)=2, a(3)=4
>> from
>> XXX
>> OOO
>> OXO
>> and I think a(4)=6.
>>
>> Wanted: enough terms to look this up in the OEIS
>> and to add it if it is not there.
>>
>
> The first terms I got are 1, 2, 4, 6, 9, 11, 14, 17, 20, 23
>
> A 8x8 matrix is
>
> O X O O O O O X
> X O O O O O O X
> O O O X O O O X
> O O X O O O O X
> O O O O O O O X
> O O O O O O O X
> O O O O O O X O
> X X X X X X O O
>
> I also computed the similar sequence where all isosceles
> triangles are forbidden.
>
> The first terms I got are 1, 2, 4, 6, 8, 10, 12, 14, 14, 16, 20
>
> A solution for 8x8:
>
> O X X X X X O X
> X O O O O O O X
> X O O O O O O O
> X O O O O O O O
> X O O O O O O O
> X O O O O O O O
> O O O O O O O O
> X X O O O O O O
>
> It seems that these two sequences are not in OEIS.
>
> Giovanni Resta
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```

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