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

israel at math.ubc.ca israel at math.ubc.ca
Thu Feb 28 02:54:59 CET 2013


I suspect "coloring" might not imply the same thing to everybody.
I'd prefer to make these matters explicit whenever possible.

Robert Israel
University of British Columbia 


On Feb 27 2013, Ron Hardin wrote:


> 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
>> 
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>> 
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