%I #4 Jan 29 2014 09:59:23

%S 81,474,474,2796,4176,2796,16588,37018,37018,16588,98368,334180,

%T 499072,334180,98368,582304,2988228,6889628,6889628,2988228,582304,

%U 3448740,26755684,93754871,148743254,93754871,26755684,3448740,20433016

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the maximum plus the upper median plus the minimum of every 2X2 subblock

%C Table starts

%C ........81..........474..........2796..........16588...........98368

%C .......474.........4176.........37018.........334180.........2988228

%C ......2796........37018........499072........6889628........93754871

%C .....16588.......334180.......6889628......148743254......3132727426

%C .....98368......2988228......93754871.....3132727426....101302533917

%C ....582304.....26755684....1276545834....66206031424...3290316038130

%C ...3448740....239823278...17430577162..1403054072202.107344851887817

%C ..20433016...2152052046..238378816652.29844445444698

%C .121047396..19284072120.3253415745852

%C .716976816.172791130750

%H R. H. Hardin, <a href="/A236640/b236640.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 21]

%F k=2: [order 72] for n>73

%e Some solutions for n=2 k=4

%e ..0..1..0..0..0....0..0..0..2..2....0..0..1..0..0....0..0..0..0..0

%e ..0..2..2..0..1....1..1..0..1..0....0..0..0..1..0....0..2..2..0..0

%e ..2..2..2..1..0....1..2..0..0..2....1..2..2..0..1....1..2..2..1..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 29 2014