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

Ron Hardin rhhardin at att.net
Mon Apr 25 03:41:33 CEST 2016


Sent.  If there were going to be a linear recurrence for column 3, I'd expect about order 18, and perhaps only for n>something, letting initial conditions settle down.  Which hasn't turned up for me.
 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: Sunday, April 24, 2016 9:04 PM
 Subject: [seqfan] Re: No isosceles triangles in a square grid, continued
   
Ron, sometimes one has more luck looking for a generating function
than for a recurrence.  If you send me the 94 terms from Column 3 I'll give
it a shot.

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 Sun, Apr 24, 2016 at 6:42 PM, Ron Hardin <rhhardin at att.net> wrote:

> T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no
> three 1s forming an isosceles right triangle
>
>
> ..1....2.....3......4......5......6......7......8......9
> ..2....6....10.....21.....34.....62....100....171....276
> ..3...10....24.....24....107....236....499...1228...2753
> ..4...21....24.....60....210....637...1840...5792..18556
> ..5...34...107....210....768...1898...8211..37402.192579
> ..6...62...236....637...1898...7468..26052.138476.831738
> ..7..100...499...1840...8211..26052.131056.648178.......
> ..8..171..1228...5792..37402.138476.648178..............
> ..9..276..2753..18556.192579.831738.....................
> .10..458..6292..54034.635086............................
> .11..740.14751.160246...................................
> .12.1211.34824..........................................
> .13.1958................................................
> .14.....................................................
> So far only cols 1 and 2 have recurrences
> Empirical for column k:
> k=1: a(n)=2*a(n-1)-a(n-2)
> k=2: a(n)=a(n-1)+3*a(n-2)-2*a(n-3)-3*a(n-4)+a(n-5)+a(n-6)
> Column 3 does not look promising for a recurrence, after 94 terms.
> work not double-checked! rhhardin at mindspring.com rhhardin at att.net (either)
>
>
>
>
>
>
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> Seqfan Mailing list - http://list.seqfan.eu/
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