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%I #8 Jul 10 2018 14:37:30
%S 9,25,65,193,513,1537,4097,12289,32769,98305,262145,786433,2097153,
%T 6291457,16777217,50331649,134217729,402653185,1073741825,3221225473,
%U 8589934593,25769803777,68719476737,206158430209,549755813889
%N Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
%C Column 2 of A209534.
%H R. H. Hardin, <a href="/A209530/b209530.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3).
%F Conjectures from _Colin Barker_, Jul 10 2018: (Start)
%F G.f.: x*(9 + 16*x - 32*x^2) / ((1 - x)*(1 - 8*x^2)).
%F a(n) = 3*2^((3*(n - 1))/2 + 3/2) + 1 for n even.
%F a(n) = 2^((3*(n - 1))/2 + 3) + 1 for n odd.
%F (End)
%e Some solutions for n=4:
%e ..0..1..2....1..0..1....2..0..2....2..1..0....1..2..1....0..1..0....2..1..0
%e ..1..2..1....2..1..2....0..2..0....1..2..1....2..1..2....1..0..1....1..2..1
%e ..0..1..0....1..2..1....2..0..2....2..1..2....1..0..1....2..1..2....0..1..0
%e ..1..0..1....2..1..2....0..2..0....1..2..1....2..1..2....1..0..1....1..2..1
%e ..0..1..2....1..2..1....2..0..2....0..1..0....1..2..1....2..1..0....0..1..2
%Y Cf. A209534.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 10 2012
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