%I #4 Jan 03 2015 11:41:44

%S 512,3328,3328,20480,33568,20480,119040,317696,317696,119040,679936,

%T 2801200,4414976,2801200,679936,3825920,24576256,57759744,57759744,

%U 24576256,3825920,21426176,212432512,751577856,1181976144,751577856

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal maximum minus antidiagonal minimum nonincreasing horizontally and nondecreasing vertically

%C Table starts

%C .....512......3328......20480.......119040.........679936..........3825920

%C ....3328.....33568.....317696......2801200.......24576256........212432512

%C ...20480....317696....4414976.....57759744......751577856.......9765667072

%C ..119040...2801200...57759744...1181976144....23704397056.....477165435664

%C ..679936..24576256..751577856..23704397056...715564083200...21859274781440

%C .3825920.212432512.9765667072.477165435664.21859274781440.1014919309654928

%H R. H. Hardin, <a href="/A253544/b253544.txt">Table of n, a(n) for n = 1..240</a>

%F Empirical for column k:

%F k=1: a(n) = 8*a(n-1) -7*a(n-2) -56*a(n-3) +120*a(n-4) -64*a(n-5)

%F k=2: [order 19]

%F k=3: [order 21]

%F k=4: [order 86] for n>93

%e Some solutions for n=2 k=4

%e ..0..1..0..0..0..0....0..0..0..0..0..1....0..1..0..0..0..0....0..1..1..1..0..0

%e ..1..1..0..0..0..0....1..1..1..0..0..0....1..1..0..0..0..1....0..1..1..0..1..0

%e ..1..0..0..1..0..0....0..1..0..1..1..1....0..0..0..1..1..0....0..0..0..0..1..1

%e ..1..1..1..1..1..0....0..1..1..0..1..1....0..1..1..1..0..0....0..0..1..1..1..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 03 2015