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

Ron Hardin rhhardin at att.net
Wed Feb 27 21:51:40 CET 2013


It's a conjecture, meaning that the series happens to agree and we call that a 
conjecture.

 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 3:49:23 PM
> Subject: [seqfan] Re: http://oeis.org/A131816 comment?
> 
> 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
> 
> _______________________________________________
> 
> Seqfan  Mailing list - http://list.seqfan.eu/
> 


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