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%I #4 Feb 04 2014 05:55:53
%S 81,245,245,777,997,777,2597,4365,4365,2597,8961,20669,25705,20669,
%T 8961,31837,102265,165317,165317,102265,31837,115561,525809,1096689,
%U 1470317,1096689,525809,115561,427093,2783881,7519165,13373885,13373885,7519165
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the minimum minus the upper median minus the lower median of every 2X2 subblock equal
%C Table starts
%C ......81.......245.........777..........2597...........8961............31837
%C .....245.......997........4365.........20669.........102265...........525809
%C .....777......4365.......25705........165317........1096689..........7519165
%C ....2597.....20669......165317.......1470317.......13373885........126858645
%C ....8961....102265.....1096689......13373885......162748369.......2072721981
%C ...31837....525809.....7519165.....126858645.....2072721981......36060137413
%C ..115561...2783881....52597313....1234905853....26807862753.....634189439561
%C ..427093..15103101...374547449...12370941453...355704138649...11585807404557
%C .1600465..83563325..2703084433..127000947377..4803893151225..217053368329433
%C .6064925.469820341.19737083525.1334978964337.66107444542473.4199505368448321
%H R. H. Hardin, <a href="/A237167/b237167.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 9]
%F k=2: [order 16]
%F k=3: [order 30]
%F k=4: [order 59]
%e Some solutions for n=3 k=4
%e ..0..2..2..2..1....0..0..1..1..1....1..1..2..1..1....0..2..1..1..2
%e ..1..2..1..2..2....1..1..0..0..2....2..2..1..0..0....1..1..0..2..1
%e ..0..2..2..2..1....0..2..1..1..1....1..1..0..1..1....0..2..1..1..0
%e ..1..2..1..2..2....1..1..2..2..2....2..2..1..2..2....2..0..1..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 04 2014