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

[Neil Sloane]

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