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%I #4 Feb 11 2014 09:57:40
%S 81,474,474,2741,4146,2741,15948,35620,35620,15948,93093,308814,
%T 449258,308814,93093,541880,2688928,5732688,5732688,2688928,541880,
%U 3152844,23395998,74265677,109962932,74265677,23395998,3152844,18356756
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the upper median plus the lower median minus the minimum of every 2X2 subblock
%C Table starts
%C ........81.........474.........2741........15948.........93093........541880
%C .......474........4146........35620.......308814.......2688928......23395998
%C ......2741.......35620.......449258......5732688......74265677.....959069036
%C .....15948......308814......5732688....109962932....2160608712...42145629006
%C .....93093.....2688928.....74265677...2160608712...65107866022.1938146594012
%C ....541880....23395998....959069036..42145629006.1938146594012
%C ...3152844...203035400..12309130146.813403060652
%C ..18356756..1763640726.158172430796
%C .106893088.15330212940
%C .622285828
%H R. H. Hardin, <a href="/A237683/b237683.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 18]
%F k=2: [order 67] for n>69
%e Some solutions for n=2 k=4
%e ..0..1..1..1..1....0..0..1..1..1....0..0..2..0..1....0..0..1..0..1
%e ..0..0..0..1..1....2..1..1..2..2....2..1..2..0..0....2..2..2..0..0
%e ..1..2..2..2..2....1..2..1..2..0....2..1..1..2..1....1..2..2..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 11 2014