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%I #4 Jan 17 2014 14:13:42
%S 81,294,294,905,722,905,2584,1372,1372,2584,7353,2660,1494,2660,7353,
%T 20800,5034,1780,1780,5034,20800,58896,9752,2478,2356,2478,9752,58896,
%U 167240,18468,3504,3496,3496,3504,18468,167240,474948,35794,4884,5036
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the upper median value of each 2X2 subblock
%C Table starts
%C ......81....294...905..2584..7353.20800.58896.167240.474948.1344000.3811120
%C .....294....722..1372..2660..5034..9752.18468..35794..67924..131474..251786
%C .....905...1372..1494..1780..2478..3504..4884...6888...9816...13920...19554
%C ....2584...2660..1780..2356..3496..5036..7320..11908..17592...25318...36632
%C ....7353...5034..2478..3496..5358..6728..9260..14016..20570...26912...36512
%C ...20800...9752..3504..5036..6728.10420.14440..23148..33704...52348...72200
%C ...58896..18468..4884..7320..9260.14440.21288..29328..41748...57760...83202
%C ..167240..35794..6888.11908.14016.23148.29328..49860..70224..108252..146640
%C ..474948..67924..9816.17592.20570.33704.41748..70224.114312..134816..190180
%C .1344000.131474.13920.25318.26912.52348.57760.108252.134816..228100..288800
%H R. H. Hardin, <a href="/A235954/b235954.txt">Table of n, a(n) for n = 1..2591</a>
%F Empirical for diagonal and column k:
%F diagonal: a(n) = 41*a(n-4) -400*a(n-8) for n>13
%F k=1: a(n) = 8*a(n-3) +36*a(n-4) +48*a(n-6) for n>9
%F k=2: a(n) = 3*a(n-3) +10*a(n-4) -12*a(n-7) -6*a(n-8) for n>12
%F k=3: a(n) = 4*a(n-4) for n>13
%F k=4: a(n) = 5*a(n-4) for n>14
%F k=5: a(n) = 4*a(n-4) for n>13
%F k=6: a(n) = 5*a(n-4) for n>14
%F k=7: a(n) = 4*a(n-4) for n>15
%e Some solutions for n=5 k=4
%e ..0..1..0..2..1....1..0..0..0..2....1..1..2..1..0....1..2..0..0..1
%e ..0..0..2..0..0....1..0..1..2..1....1..2..0..0..0....2..1..0..1..2
%e ..1..2..1..0..1....0..0..2..1..0....2..1..0..1..2....0..0..0..2..1
%e ..2..0..0..0..2....1..2..0..0..0....0..0..0..2..1....0..1..2..1..0
%e ..1..0..1..2..1....2..1..0..2..1....0..1..2..0..0....1..2..0..0..0
%e ..0..0..2..0..0....0..0..0..1..2....1..2..1..0..1....2..1..0..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 17 2014
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