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Number of n X 4 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 #8 Oct 07 2018 08:25:35

%S 14,386,11486,342626,10221326,304926626,9096692126,271376130626,

%T 8095800458126,241517133090626,7205034990428126,214943464047390626,

%U 6412278746469578126,191293645073850390626,5706747958483163828126

%N Number of n X 4 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="/A233094/b233094.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) - 35*a(n-2) + 5*a(n-3).

%F Conjectures from _Colin Barker_, Oct 07 2018: (Start)

%F G.f.: 2*x*(7 - 24*x + 5*x^2) / ((1 - x)*(1 - 30*x + 5*x^2)).

%F a(n) = (110 + (15-2*sqrt(55))^n*(55+sqrt(55)) - (-55+sqrt(55))*(15+2*sqrt(55))^n) / 110.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 4 of A233098.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 04 2013