%I #8 Oct 03 2018 05:54:47

%S 4,14,46,130,410,1194,3722,10942,33806,100142,307418,915594,2797794,

%T 8365310,25477518,76390718,232103802,697334282,2115143362,6363967678,

%U 19279364750,58067541662,175757663194,529761502474,1602452666114

%N Number of n X 3 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.

%H R. H. Hardin, <a href="/A232060/b232060.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 7*a(n-2) - 3*a(n-3) + 3*a(n-4) - 7*a(n-5) + 2*a(n-6) - 2*a(n-7) + 2*a(n-8).

%F Empirical g.f.: 2*x*(1 + x + x^2)*(2 + 3*x - 3*x^2 - x^3 - 2*x^4 + 2*x^5) / (1 - x - 7*x^2 + 3*x^3 - 3*x^4 + 7*x^5 - 2*x^6 + 2*x^7 - 2*x^8). - _Colin Barker_, Oct 03 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A232065.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 17 2013