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Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
1

%I #9 Oct 07 2018 08:02:50

%S 5,65,941,13721,200165,2920145,42601181,621496841,9066845525,

%T 132273701825,1929704454221,28151924602361,410700642310085,

%U 5991598087037105,87409767451696061,1275196923253218281

%N Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

%H R. H. Hardin, <a href="/A233093/b233093.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 21*a(n-2) + 6*a(n-3).

%F Empirical g.f.: x*(5 - 15*x + 6*x^2) / ((1 - x)*(1 - 15*x + 6*x^2)). - _Colin Barker_, Oct 07 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 3 of A233098.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 04 2013