%I #4 Feb 07 2014 05:28:28

%S 256,1314,1314,7172,11988,7172,41062,114034,114034,41062,239176,

%T 1153778,1794402,1153778,239176,1413864,11725568,30590608,30590608,

%U 11725568,1413864,8412540,121195320,514064312,902019154,514064312,121195320

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the maximum plus the upper median minus the lower median of every 2X2 subblock equal

%C Table starts

%C .......256.........1314...........7172.............41062..............239176

%C ......1314........11988.........114034...........1153778............11725568

%C ......7172.......114034........1794402..........30590608...........514064312

%C .....41062......1153778.......30590608.........902019154.........25829139276

%C ....239176.....11725568......514064312.......25829139276.......1235023110530

%C ...1413864....121195320.....8872195706......769041196608......62405831529234

%C ...8412540...1254144270...152180119484....22613650645686....3084781518411320

%C ..50339772..13055041806..2639996468928...676946049444764..156724811087291634

%C .302048100.135960274878.45688402987094.20153268873982042.7881021180947620852

%H R. H. Hardin, <a href="/A237398/b237398.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 38]

%F k=2: [order 97]

%e Some solutions for n=2 k=4

%e ..0..2..3..3..2....0..2..3..1..3....0..2..3..1..2....0..0..3..2..2

%e ..1..3..0..2..3....1..3..1..2..1....2..1..2..2..0....1..2..2..1..3

%e ..0..2..3..3..2....3..2..3..0..3....0..2..3..1..2....2..3..0..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 07 2014