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%I #4 Feb 02 2014 07:19:45
%S 81,360,360,1600,2376,1600,7200,15552,15552,7200,32400,104976,149632,
%T 104976,32400,144000,699840,1513728,1513728,699840,144000,640000,
%U 4618944,14963200,23825664,14963200,4618944,640000,2880000,30233088,145732608
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the lower median minus the upper median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C .......81........360..........1600............7200.............32400
%C ......360.......2376.........15552..........104976............699840
%C .....1600......15552........149632.........1513728..........14963200
%C .....7200.....104976.......1513728........23825664.........363916800
%C ....32400.....699840......14963200.......363916800........8552563200
%C ...144000....4618944.....145732608......5454273024......192222720000
%C ...640000...30233088....1406076928.....80675315712.....4279521280000
%C ..2880000..204073344...14212288512...1304215105536...109212364800000
%C .12960000.1360488960..140607692800..20389194547200..2683631554560000
%C .57600000.8979227136.1372136620032.312112856088576.62224920576000000
%H R. H. Hardin, <a href="/A236997/b236997.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: a(n) = 400*a(n-4)
%F k=2: a(n) = 1944*a(n-4)
%F k=3: a(n) = 10*a(n-1) +8704*a(n-4) -87040*a(n-5)
%F k=4: a(n) = 158112*a(n-4) -7941224448*a(n-8) +124128835928064*a(n-12)
%F k=5: [order 16]
%F k=6: [order 17]
%F k=7: [order 15]
%e Some solutions for n=3 k=4
%e ..0..0..0..1..0....0..0..0..1..2....0..0..1..1..2....0..0..1..1..0
%e ..2..1..1..1..0....0..2..1..2..0....2..1..0..1..2....2..1..0..1..2
%e ..2..1..0..2..2....0..1..2..0..0....1..0..0..1..1....1..0..2..1..1
%e ..2..0..1..2..2....2..1..1..1..0....0..0..0..0..0....0..2..0..0..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 02 2014
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