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%I #9 Jul 14 2018 02:47:25
%S 34,258,1956,14832,112464,852768,6466176,49030272,371775744,
%T 2819017728,21375415296,162080704512,1228989210624,9318903717888,
%U 70661292834816,535794601623552,4062703123759104,30805753962037248,233586961257332736
%N Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at most one duplicate clockwise edge difference.
%C Column 1 of A209951.
%H R. H. Hardin, <a href="/A209944/b209944.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) + 12*a(n-2).
%F Conjectures from _Colin Barker_, Jul 14 2018: (Start)
%F G.f.: 2*x*(17 + 27*x) / (1 - 6*x - 12*x^2).
%F a(n) = ((3-sqrt(21))^n*(-41+9*sqrt(21)) + (3+ sqrt(21))^n*(41+9*sqrt(21))) / (4*sqrt(21)).
%F (End)
%e Some solutions for n=4:
%e ..2..0....0..1....1..1....2..1....2..1....2..1....2..1....2..2....1..2....2..0
%e ..2..2....2..0....2..0....0..0....0..2....2..2....0..2....1..2....0..2....1..2
%e ..0..1....1..2....0..1....1..1....1..1....1..2....1..2....2..2....0..2....0..2
%e ..2..1....2..0....2..2....1..0....1..2....0..2....2..2....1..2....2..2....1..0
%e ..2..1....0..1....2..1....2..2....1..1....2..2....1..0....1..1....0..2....2..2
%Y Cf. A209951.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 16 2012
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