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Number of nX3 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors
2

%I #5 Mar 31 2012 12:36:40

%S 5,178,9880,583813,34679839,2060918000,122478253815,7278777317468,

%T 432571571252989,25707362563355693,1527766813187552208,

%U 90793889493222901029,5395804057415427972197,320668071260622898796015

%N Number of nX3 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors

%C Column 3 of A200801

%H R. H. Hardin, <a href="/A200796/b200796.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 60*a(n-1) -17*a(n-2) -964*a(n-3) -2509*a(n-4) +968*a(n-5) +23125*a(n-6) +31652*a(n-7) -4566*a(n-8) -17118*a(n-9) -29646*a(n-10) -74826*a(n-11) -64125*a(n-12) -13932*a(n-13) +4131*a(n-14) +1458*a(n-15) for n>16

%e Some solutions for n=4

%e ..0..0..0....0..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1

%e ..1..2..2....0..2..2....1..2..2....2..0..1....1..2..0....1..2..0....1..2..0

%e ..0..0..3....1..2..3....1..2..2....2..3..3....3..0..0....3..1..1....1..3..3

%e ..2..3..2....0..0..0....2..0..1....3..3..2....3..0..1....0..3..2....3..2..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 22 2011