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

Neil Sloane njasloane at gmail.com
Mon Apr 25 05:16:51 CEST 2016


I had no luck looking for a g.f. No surprise, since you didn't
find anything!

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 9:41 PM, Ron Hardin <rhhardin at att.net> wrote:

> 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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> >
>
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>
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