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%I #4 Apr 10 2014 17:58:25
%S 1,1,1,2,5,2,5,27,27,5,14,193,461,193,14,41,1391,7980,7980,1391,41,
%T 122,10072,138562,332412,138562,10072,122,365,72941,2406061,13844254,
%U 13844254,2406061,72941,365,1094,528283,41780245,576606991,1382959986
%N T(n,k)=Number of nXk 0..3 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order
%C Table starts
%C ...1......1.........2.............5...............14..................41
%C ...1......5........27...........193.............1391...............10072
%C ...2.....27.......461..........7980...........138562.............2406061
%C ...5....193......7980........332412.........13844254...........576606991
%C ..14...1391....138562......13844254.......1382959986........138151966465
%C ..41..10072...2406061.....576606991.....138151966465......33101173163229
%C .122..72941..41780245...24015292771...13800783910238....7931008306049886
%C .365.528283.725496762.1000221764213.1378639013959376.1900262865283299277
%H R. H. Hardin, <a href="/A240706/b240706.txt">Table of n, a(n) for n = 1..127</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) = 15*a(n-1) +40*a(n-2) +22*a(n-3) -60*a(n-4) -40*a(n-5) -21*a(n-6) +45*a(n-7)
%F k=4: [order 20]
%F k=5: [order 54]
%e Some solutions for n=3 k=4
%e ..0..1..2..3....0..1..2..3....0..1..0..2....0..1..0..2....0..1..2..1
%e ..3..2..0..2....1..0..3..0....2..0..2..0....3..2..1..0....3..0..3..2
%e ..2..0..2..1....2..3..0..2....3..2..3..2....1..3..2..1....0..2..0..3
%Y Column 1 is A007051(n-2)
%Y Column 2 is A240637
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Apr 10 2014