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%I #4 Jan 31 2014 05:42:01
%S 81,474,474,2797,4170,2797,16360,36260,36260,16360,95961,315666,
%T 471689,315666,95961,562284,2750070,6140316,6140316,2750070,562284,
%U 3296708,24023328,80610053,121728522,80610053,24023328,3296708,19317952
%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 minus the lower median of every 2X2 subblock
%C Table starts
%C ........81.........474.........2797........16360.........95961........562284
%C .......474........4170........36260.......315666.......2750070......24023328
%C ......2797.......36260.......471689......6140316......80610053....1058879504
%C .....16360......315666......6140316....121728522....2437062052...49038860968
%C .....95961.....2750070.....80610053...2437062052...75317723364.2336323498652
%C ....562284....24023328...1058879504..49038860968.2336323498652
%C ...3296708...209304200..13857495596.976380249206
%C ..19317952..1823484380.181102978376
%C .113216324.15890176976
%C .663531280
%H R. H. Hardin, <a href="/A236780/b236780.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 17]
%F k=2: [order 62]
%e Some solutions for n=2 k=4
%e ..0..2..0..2..2....0..2..0..0..0....0..0..1..0..2....0..0..0..1..0
%e ..1..0..2..2..2....2..2..0..0..1....0..0..2..1..2....1..2..2..0..0
%e ..1..1..2..2..1....2..2..2..2..1....1..2..2..1..0....0..1..0..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 31 2014