[seqfan] Re: http://oeis.org/A131816 comment?

Neil Sloane njasloane at gmail.com
Wed Feb 27 21:49:17 CET 2013


Ron, I expanded the comments in A131816 (and made a few editorial
improvements).

Do you a proof that your array is the same as A131816, or is it a
conjecture?

Neil



On Wed, Feb 27, 2013 at 3:28 PM, Ron Hardin <rhhardin at att.net> wrote:

> Hasler took care of it neatly.
>
> fill the array with 0's and 1's
>
> there must never be 3 adjacent identical values making a corner, only same
> values in a straight line.
>
> it seemed like mentioning both tiling and coloring would imply all of
> that, ie
> colored tiles covering the array with no adjacent same colors.
>
>  rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>
> ----- Original Message ----
> > From: Neil Sloane <njasloane at gmail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Sent: Wed, February 27, 2013 3:23:47 PM
> > Subject: [seqfan] Re: http://oeis.org/A131816 comment?
> >
> > Ron, I suppose the right way to handle this would be to add a comment
> > to  A131816.
> >
> > I would do it myself, but I confess
> > I do not understand the  definition of your version.
> >
> > T(n,k)=Number of nXk 0..1 arrays colored with  only straight tiles, and
> new
> > values 0..1 introduced in row major order
> > (ie  no equal adjacent values form a corner)
> >
> > I totally do not understand  that!
> >
> > If you make it clearer, then add a comment to A131816  saying:
> >
> > This sequence is the same (or, appears to be
> > the same, or, is  conjectured to be the same)  as the sequence obtained
> by
> > reading the  array U(n,k) by antidiagonals, where U(n,k) is the number of
> > ... . This array  begins as follows:
> > then give a few rows of the array, followed by your  examples for the 4,4
> > case.
> >
> > Neil
> >
> > On Tue, Feb 26, 2013 at 4:53  PM, Ron Hardin <rhhardin at att.net> wrote:
> >
> > >  Question of what comment to add:
> > >
> > > http://oeis.org/A131816
> > > Triangle read by rows: A130321 + A059268 -  A000012 as infinite lower
> > > triangular
> > > matrices
> > >
> > > %e  A131816 First few rows of the triangle are:
> > > %e A131816 1;
> > > %e  A131816 2, 2;
> > > %e A131816 4, 3, 4;
> > > %e A131816 8, 5, 5, 8;
> > >  %e A131816 16, 9, 7, 9, 16;
> > > %e A131816 32, 17, 11, 11, 17, 32;
> > >  %e A131816 64, 33, 19, 15, 19, 33, 64;
> > > %e A131816 128, 65, 35, 23, 23,  35, 65, 128;
> > >
> > > Compare new /tmp/dar
> > > T(n,k)=Number of nXk  0..1 arrays colored with only straight tiles,
> and new
> > > values 0..1  introduced in row major order
> > > (ie no equal adjacent values form a  corner)
> > >
> > > Table starts
> > >  ....1....2....4....8..16..32..64.128.256.512.1024.2048.4096.8192
> > >  ....2....3....5....9..17..33..65.129.257.513.1025.2049.4097.....
> > >  ....4....5....7...11..19..35..67.131.259.515.1027.2051..........
> > >  ....8....9...11...15..23..39..71.135.263.519.1031...............
> > >  ...16...17...19...23..31..47..79.143.271.527....................
> > >  ...32...33...35...39..47..63..95.159.287........................
> > >  ...64...65...67...71..79..95.127.191............................
> > >  ..128..129..131..135.143.159.191................................
> > >  ..256..257..259..263.271.287....................................
> > >  ..512..513..515..519.527........................................
> > >  .1024.1025.1027.1031............................................
> > >  .2048.2049.2051.................................................
> > >
> > >  The A131816 rows are the /tmp/dar antidiagonals!
> > >
> > > Some solutions  for n=4 k=4
> > >  ..0..1..0..1....0..1..0..0....0..0..0..1....0..0..1..1....0..1..0..1..
> > >  ..1..0..1..0....1..0..1..1....1..1..1..0....1..1..0..0....1..0..1..0..
> > >  ..1..0..1..0....0..1..0..0....0..0..0..1....0..0..1..1....0..1..0..1..
> > >  ..0..1..0..1....1..0..1..1....1..1..1..0....1..1..0..0....0..1..0..1..
> > >
> > >  The formula given for A131816 is
> > >
> > > t(n,m)=((2^(m + 1) - 1) +  (2^(n - m + 1) - 1))/2
> > >
> > > Translating that to  /tmp/dar
> > >
> > > T(n,k)=((2^n - 1) + (2^k - 1))/2
> > >
> > > The  question is what comment to add to A131816 (and does somebody
> want to
> > >  add
> > > it).
> > >
> > >
> > >  rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> > >
> > >
> > >  _______________________________________________
> > >
> > > Seqfan Mailing  list - http://list.seqfan.eu/
> > >
> >
> >
> >
> > --
> > Dear Friends, I have  now retired from AT&T. New coordinates:
> >
> > Neil J. A. Sloane, President,  OEIS Foundation
> > 11 South Adelaide Avenue, Highland Park, NJ 08904,  USA
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
> > Seqfan  Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

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


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