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%I #4 Feb 14 2014 07:57:31
%S 81,336,336,1414,1944,1414,6030,11454,11454,6030,25525,68830,95470,
%T 68830,25525,107272,405758,811498,811498,405758,107272,453088,2385956,
%U 6710651,9902380,6710651,2385956,453088,1919632,14144254,55582616,115821338
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the upper median plus the lower median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C .......81........336.........1414...........6030............25525
%C ......336.......1944........11454..........68830...........405758
%C .....1414......11454........95470.........811498..........6710651
%C .....6030......68830.......811498........9902380........115821338
%C ....25525.....405758......6710651......115821338.......1893170622
%C ...107272....2385956.....55582616.....1360467556......31199205700
%C ...453088...14144254....466228162....16245005586.....524709935082
%C ..1919632...84226372...3923377300...195628632968....8912673852976
%C ..8117752..497945422..32640488162..2309260676524..147501045116290
%C .34231344.2940973430.271793432028.27312310344552.2450909073999912
%H R. H. Hardin, <a href="/A237868/b237868.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 14]
%F k=2: [order 33]
%e Some solutions for n=3 k=4
%e ..0..1..0..0..2....0..0..2..0..0....0..0..0..2..2....0..0..1..1..0
%e ..1..1..0..0..1....1..1..1..0..0....0..1..1..1..2....2..2..2..2..2
%e ..2..1..1..1..2....0..1..2..1..2....1..0..1..1..0....2..1..1..2..2
%e ..1..0..0..2..2....1..0..1..1..0....2..1..0..2..2....2..1..2..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 14 2014
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