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%I #4 Feb 17 2014 08:06:25
%S 81,340,340,1440,1944,1440,6064,10812,10812,6064,25948,61668,81524,
%T 61668,25948,109200,352180,621780,621780,352180,109200,466296,1999804,
%U 4837484,6698520,4837484,1999804,466296,1962720,11359816,36440340,70363916
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C .......81........340.........1440..........6064...........25948
%C ......340.......1944........10812.........61668..........352180
%C .....1440......10812........81524........621780.........4837484
%C .....6064......61668.......621780.......6698520........70363916
%C ....25948.....352180......4837484......70363916......1021660750
%C ...109200....1999804.....36440340.....735878108.....14397005860
%C ...466296...11359816....282305082....7744640808....209192156822
%C ..1962720...64650988...2134998732...81468910084...2964129769048
%C ..8385248..367695852..16538701324..855621962264..42974757198114
%C .35292928.2090439976.124970610892.8992624643448.608837111985680
%H R. H. Hardin, <a href="/A238046/b238046.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-2) +152*a(n-4) +472*a(n-6) +384*a(n-8)
%F k=2: [order 13]
%F k=3: [order 50]
%e Some solutions for n=3 k=4
%e ..0..1..1..0..2....0..0..2..2..1....0..1..1..1..0....0..0..2..0..1
%e ..0..1..0..2..0....0..1..2..0..0....0..1..2..2..1....0..1..0..2..0
%e ..0..0..2..0..1....0..2..2..1..0....1..1..2..0..0....0..2..1..0..0
%e ..1..1..1..2..1....1..1..1..0..2....2..2..2..1..0....1..1..2..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 17 2014
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