%I #4 Jan 01 2015 06:57:50
%S 81,414,414,1388,1975,1388,3639,4782,4782,3639,8501,8554,7782,8554,
%T 8501,19701,15220,11147,11147,15220,19701,48293,31630,19254,15730,
%U 19254,31630,48293,126357,74324,39463,26831,26831,39463,74324,126357,346997,188438
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically
%C Table starts
%C .....81.....414....1388....3639....8501...19701...48293..126357...346997
%C ....414....1975....4782....8554...15220...31630...74324..188438...502364
%C ...1388....4782....7782...11147...19254...39463...89556..218326...561564
%C ...3639....8554...11147...15730...26831...52912..114717..266911...656997
%C ...8501...15220...19254...26831...44242...83003..170184..373130...864720
%C ..19701...31630...39463...52912...83003..147332..285681..590963..1287225
%C ..48293...74324...89556..114717..170184..285681..526430.1036512..2142374
%C .126357..188438..218326..266911..373130..590963.1036512.1956194..3881256
%C .346997..502364..561564..656997..864720.1287225.2142374.3881256..7444718
%C .982677.1387310.1505134.1694263.2104994.2936843.4611192.7988474.14828736
%H R. H. Hardin, <a href="/A253456/b253456.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10
%F k=2..9: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>9
%F Empirical for column k:
%F k=1: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7
%F k=2: a(n) = 529*3^(n-3) + 444*2^(n-1) + 3059 for n>6
%F k=3: a(n) = 529*3^(n-3) + 673*2^(n-1) + 3635 for n>6
%F k=4: a(n) = 529*3^(n-3) + 1039*2^(n-1) + 5372 for n>6
%F k=5: a(n) = 529*3^(n-3) + 1832*2^(n-1) + 10087 for n>6
%F k=6: a(n) = 529*3^(n-3) + 3431*2^(n-1) + 23248 for n>6
%F k=7: a(n) = 529*3^(n-3) + 6631*2^(n-1) + 59197 for n>6
%F k=8: a(n) = 529*3^(n-3) + 13031*2^(n-1) + 159679 for n>6
%F k=9: a(n) = 529*3^(n-3) + 25831*2^(n-1) + 446341 for n>6
%e Some solutions for n=4 k=4
%e ..0..1..2..2..2....0..2..1..2..1....0..1..1..1..1....1..2..0..0..1
%e ..0..0..1..1..1....2..2..1..2..1....2..2..2..2..2....1..2..0..0..1
%e ..1..0..1..1..1....2..2..1..2..1....2..1..1..1..1....1..2..0..0..1
%e ..1..0..1..1..1....1..1..0..1..0....1..0..0..0..1....1..2..0..0..1
%e ..1..0..1..1..2....1..1..0..1..0....1..0..0..0..2....1..2..0..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 01 2015
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