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%I #4 Apr 16 2014 07:05:16
%S 1,2,2,5,14,5,14,113,113,14,41,953,2612,953,41,122,8037,60340,60340,
%T 8037,122,365,67774,1394492,3829419,1394492,67774,365,1094,571530,
%U 32228144,242964166,242964166,32228144,571530,1094,3281,4819638,744822776
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..2 introduced in row major order
%C Table starts
%C ...1......2.........5...........14...............41.................122
%C ...2.....14.......113..........953.............8037...............67774
%C ...5....113......2612........60340..........1394492............32228144
%C ..14....953.....60340......3829419........242964166.........15415566961
%C ..41...8037...1394492....242964166......42319480270.......7371117761274
%C .122..67774..32228144..15415566961....7371117761274....3524558549098471
%C .365.571530.744822776.978087593971.1283885768594047.1685292182142705704
%H R. H. Hardin, <a href="/A241114/b241114.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F k=2: a(n) = 8*a(n-1) +4*a(n-2) -2*a(n-3) -8*a(n-4) for n>6
%F k=3: [order 12] for n>13
%F k=4: [order 42] for n>43
%e Some solutions for n=3 k=4
%e ..0..0..1..2....0..0..1..1....0..0..0..0....0..1..0..2....0..1..1..2
%e ..0..2..2..1....1..2..2..1....0..1..2..0....0..2..2..0....0..1..2..0
%e ..2..1..0..2....1..1..1..2....2..1..1..2....1..0..0..1....0..2..0..2
%Y Column 1 is A007051(n-1)
%Y Column 2 is A199649
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 16 2014
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