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

Zak Seidov zakseidov at mail.ru
Fri Apr 22 19:10:59 CEST 2016

``` 18-solution for 8x8 square?
See fig.
Zak

>Пятница, 22 апреля 2016, 17:21 +03:00 от Neil Sloane <njasloane at gmail.com>:
>
>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.
>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/
>>
>
>--
>Seqfan Mailing list -  http://list.seqfan.eu/

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