[seqfan] Re: No isosceles triangles in a square grid, continued

Ron Hardin rhhardin at att.net
Wed Apr 27 18:03:45 CEST 2016


Simple to do, yes.  I can't reach far into the diagonal however owing to a memory blowup, which stops the antidiagonal search (which is the reason for doing columns independently of antidiagonal search).
 rhhardin at mindspring.com rhhardin at att.net (either)

 
      From: Neil Sloane <njasloane at gmail.com>
 To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
 Sent: Wednesday, April 27, 2016 11:48 AM
 Subject: [seqfan] Re: No isosceles triangles in a square grid, continued
   
Ron, would it be a simple matter to run
Tminusone(n,k)=Number of nXk 0..1 arrays with exactly n+k-1 having value 1
and no three 1s forming an isosceles triangle
(where I have replaced n+k-2 with n+k-1) ?

(After the present run has finished, of course)

It will have mostly zero entries, and will be another check on A271914.

In fact, it would also be interesting to look at
Tbeyondthe pale(n,k)=Number of nXk 0..1 arrays with exactly n+k having
value 1 and no three 1s forming an isosceles triangle
where every entry should be zero


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 Wed, Apr 27, 2016 at 11:18 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Ron, it is really good to have that confirmation of the first zero entry
>
> Can you add that array too? (and tell me the A-numbers for both)
>
> 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 Wed, Apr 27, 2016 at 9:57 AM, Ron Hardin <rhhardin at att.net> wrote:
>
>> Ok, I get something that looks right vs A271914 then I think
>>
>> T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no
>> three 1s forming an isosceles triangle
>>
>> Table starts
>> ..1..2..3..4..5..6..7..8..9.10.11.12.13.14.15
>> ..2..6.10.21.14.28.18.29.22.32.26.36.30.40...
>> ..3.10.12..4.14.36.23.44.14.48.14.52.14......
>> ..4.21..4..8..4.37..8.44..8.44..0.34.........
>> ..5.14.14..4..4..4.10.80.37.56..4............
>> ..6.28.36.37..4..8..4.22..0.34...............
>> ..7.18.23..8.10..4..4..4..2..................
>> ..8.29.44.44.80.22..4........................
>> ..9.22.14..8.37..0...........................
>> .10.32.48.44.56..............................
>> .11.26.14..0.................................
>> .12.36.52....................................
>> .13.30.......................................
>> .14..........................................
>>  Note no solution for (4,11)
>> rhhardin at mindspring.com rhhardin at att.net (either)
>>
>>
>>      From: Neil Sloane <njasloane at gmail.com>
>>  To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>  Sent: Wednesday, April 27, 2016 8:43 AM
>>  Subject: [seqfan] Re: No isosceles triangles in a square grid, continued
>>
>> No, the triangle must have nonzero area
>>
>> 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 Wed, Apr 27, 2016 at 8:41 AM, Ron Hardin <rhhardin at att.net> wrote:
>>
>> > Question, do 3 consecutive 1's in a row count as an isosceles triangle?
>> > rhhardin at mindspring.com rhhardin at att.net (either)
>> >
>> >
>> >      From: Ron Hardin <rhhardin at att.net>
>> >  To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> >  Sent: Wednesday, April 27, 2016 8:12 AM
>> >  Subject: [seqfan] Re: No isosceles triangles in a square grid,
>> continued
>> >
>> > Okay, good.  I should drop the "right triangle" constraint.
>> >
>> >
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>

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