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%I #4 Jan 31 2014 07:35:05
%S 81,327,327,1386,2211,1386,6093,15254,15254,6093,27079,109205,168564,
%T 109205,27079,121590,786609,1949236,1949236,786609,121590,549173,
%U 5747502,22695802,36874967,22695802,5747502,549173,2495215,42215123,269108894
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the minimum minus the lower median of every 2X2 subblock equal
%C Table starts
%C .......81.........327..........1386.............6093..............27079
%C ......327........2211.........15254...........109205.............786609
%C .....1386.......15254........168564..........1949236...........22695802
%C .....6093......109205.......1949236.........36874967..........701424751
%C ....27079......786609......22695802........701424751........21755065689
%C ...121590.....5747502.....269108894......13643698414.......692297987804
%C ...549173....42215123....3207539588.....266389315989.....22074170878628
%C ..2495215...312592339...38599508572....5258599354623....712496076337427
%C .11389842..2324534826..466275664500..104078580277828..23029391418201045
%C .52223381.17376767995.5664487537556.2072356525693189.749146158534878661
%H R. H. Hardin, <a href="/A236828/b236828.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 14]
%F k=2: [order 30]
%F k=3: [order 84]
%e Some solutions for n=3 k=4
%e ..0..0..2..0..2....0..0..1..2..2....0..0..0..1..0....0..0..2..0..1
%e ..0..1..1..1..1....0..1..0..1..0....1..0..1..0..0....0..2..0..2..0
%e ..1..2..0..0..2....0..1..0..0..1....1..2..1..0..1....0..0..2..0..2
%e ..2..2..1..1..1....1..2..1..1..0....1..0..1..0..1....2..0..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 31 2014