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%I #4 Jan 18 2014 15:33:13
%S 81,384,384,1848,2460,1848,8856,14980,14980,8856,42724,93640,116786,
%T 93640,42724,205660,595416,965344,965344,595416,205660,990076,3752292,
%U 8289258,11384132,8289258,3752292,990076,4760380,23516900,68613596
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the difference of the upper median and the lower median in each 2X2 subblock
%C Table starts
%C ........81........384.........1848...........8856............42724
%C .......384.......2460........14980..........93640...........595416
%C ......1848......14980.......116786.........965344..........8289258
%C ......8856......93640.......965344.......11384132........135945364
%C .....42724.....595416......8289258......135945364.......2282216166
%C ....205660....3752292.....68613596.....1562942580......36483535032
%C ....990076...23516900....570818506....18041076392.....590896758666
%C ...4760380..147865936...4747089488...210792493144....9608835890536
%C ..22914572..931263424..39848021722..2453096266960..156707889598596
%C .110251484.5858644440.330427763000.28456755301120.2530161441550248
%H R. H. Hardin, <a href="/A236035/b236035.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 10]
%F k=2: [order 19]
%F k=3: [order 92] for n>95
%e Some solutions for n=3 k=4
%e ..0..1..1..2..2....0..2..1..2..1....0..1..1..2..2....0..0..1..1..2
%e ..0..1..0..0..2....0..2..1..0..2....0..2..1..2..2....0..1..0..1..2
%e ..0..0..2..0..1....1..0..1..0..0....2..2..0..1..0....2..2..1..0..1
%e ..1..1..1..0..0....0..0..2..1..2....0..0..0..1..1....0..2..1..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 18 2014