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%I #4 Feb 15 2014 17:29:31
%S 256,1584,1584,9892,14564,9892,63476,133528,133528,63476,406468,
%T 1282504,1907520,1282504,406468,2591160,12149024,27873820,27873820,
%U 12149024,2591160,16574240,115206520,405401852,636891488,405401852,115206520
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median plus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C ........256.........1584............9892............63476............406468
%C .......1584........14564..........133528..........1282504..........12149024
%C .......9892.......133528.........1907520.........27873820.........405401852
%C ......63476......1282504........27873820........636891488.......14163256928
%C .....406468.....12149024.......405401852......14163256928......488835819834
%C ....2591160....115206520......5873296416.....319272033708....16925434187136
%C ...16574240...1092851528.....85701783182....7170378195892...590192559141494
%C ..105734776..10375258140...1241851571792..161382511774196.20435454685816288
%C ..676470380..98442896216..18123171520244.3629106051378200
%C .4314907116.934214824740.262625441797028
%H R. H. Hardin, <a href="/A237921/b237921.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 18]
%F k=2: [order 56]
%e Some solutions for n=2 k=4
%e ..0..0..1..1..1....0..2..1..2..1....0..0..0..2..1....0..2..1..2..1
%e ..0..0..1..0..0....2..0..2..3..3....0..1..3..0..2....1..3..2..1..0
%e ..2..1..2..0..3....1..3..2..3..2....3..0..1..0..2....3..0..3..2..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 15 2014