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

[Ron Hardin]

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)