%I #6 Dec 01 2014 12:57:53

%S 40,133,133,369,416,369,919,1002,1002,919,2129,2264,1997,2264,2129,

%T 4699,4786,4110,4110,4786,4699,10033,9786,8050,8008,8050,9786,10033,

%U 20947,19548,15830,14753,14753,15830,19548,20947,43077,38674,30770,27738,25597

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements

%C Table starts

%C ....40....133....369....919...2129...4699...10033...20947...43077...87703

%C ...133....416...1002...2264...4786...9786...19548...38674...76196..150192

%C ...369...1002...1997...4110...8050..15830...30770...60088..117492..230956

%C ...919...2264...4110...8008..14753..27738...51679...97758..186223..359276

%C ..2129...4786...8050..14753..25597..46023...82431..151567..282371..536601

%C ..4699...9786..15830..27738..46023..79226..135959..240780..434193..804400

%C .10033..19548..30770..51679..82431.135959..223663..380641..662361.1191797

%C .20947..38674..60088..97758.151567.240780..380641..620524.1035365.1793398

%C .43077..76196.117492.186223.282371.434193..662361.1035365.1653313.2742539

%C .87703.150192.230956.359276.536601.804400.1191797.1793398.2742539.4340190

%H R. H. Hardin, <a href="/A251137/b251137.txt">Table of n, a(n) for n = 1..543</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-1) -8*a(n-2) +2*a(n-3) +7*a(n-4) -7*a(n-5) +2*a(n-6)

%F k=2: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>9

%F k=3: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

%F k=4: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

%F k=5: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

%F k=6: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

%F k=7: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>10

%e Some solutions for n=4 k=4

%e ..0..1..0..2..2....0..0..2..0..2....1..1..1..1..1....1..1..1..2..2

%e ..0..1..0..0..0....0..0..2..0..2....1..0..0..0..0....0..0..0..0..0

%e ..0..1..0..0..0....1..0..2..0..2....2..0..0..0..0....1..1..1..1..1

%e ..0..1..0..0..0....1..0..2..0..1....2..0..0..0..0....1..0..0..0..0

%e ..2..2..1..1..1....2..1..2..0..1....2..0..0..0..0....2..1..1..1..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 30 2014