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%I #4 Apr 09 2014 19:09:04
%S 1,1,1,2,5,2,5,27,27,5,14,193,462,193,14,41,1391,7993,7993,1391,41,
%T 122,10072,138882,333308,138882,10072,122,365,72941,2413198,13897353,
%U 13897353,2413198,72941,365,1094,528283,41931738,579476701,1390560136
%N T(n,k)=Number of nXk 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order
%C Table starts
%C ....1........1............2................5...................14
%C ....1........5...........27..............193.................1391
%C ....2.......27..........462.............7993...............138882
%C ....5......193.........7993...........333308.............13897353
%C ...14.....1391.......138882.........13897353...........1390560136
%C ...41....10072......2413198........579476701.........139138607313
%C ..122....72941.....41931738......24162243789.......13922129807222
%C ..365...528283....728606311....1007486056500.....1393040370960551
%C .1094..3826157..12660271050...42008844856285...139386826311366370
%C .3281.27711478.219985006177.1751630302786777.13946966455660995272
%H R. H. Hardin, <a href="/A240642/b240642.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) for n>3
%F k=2: a(n) = 6*a(n-1) +10*a(n-2) -6*a(n-3) -9*a(n-4) for n>6
%F k=3: a(n) = 14*a(n-1) +54*a(n-2) +82*a(n-3) -14*a(n-4) -54*a(n-5) -81*a(n-6)
%F k=4: [order 14]
%F k=5: [order 31]
%e Some solutions for n=3 k=4
%e ..0..1..0..2....0..1..2..0....0..1..2..0....0..1..0..1....0..1..0..1
%e ..1..0..1..0....1..2..0..1....2..0..3..2....1..2..3..2....1..2..1..2
%e ..0..2..0..1....3..0..3..2....3..1..2..3....3..1..2..3....2..0..2..1
%Y Column 1 is A007051(n-2)
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Apr 09 2014
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