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A207656 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

%I A207656 #9 Jun 25 2018 07:53:46
%S A207656 6,36,84,198,474,1140,2748,6630,16002,38628,93252,225126,543498,
%T A207656 1312116,3167724,7647558,18462834,44573220,107609268,259791750,
%U A207656 627192762,1514177268,3655547292,8825271846,21306090978,51437453796,124180998564
%N A207656 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.
%C A207656 Column 3 of A207661.
%H A207656 R. H. Hardin, <a href="/A207656/b207656.txt">Table of n, a(n) for n = 1..210</a>
%F A207656 Empirical: a(n) = 3*a(n-1) - a(n-2) - a(n-3) for n>4.
%F A207656 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207656 G.f.: 6*x*(1 + 3*x - 3*x^2 - 2*x^3) / ((1 - x)*(1 - 2*x - x^2)).
%F A207656 a(n) = (3/2)*(2 + (1-2*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(1+2*sqrt(2))) for n>1.
%F A207656 (End)
%e A207656 Some solutions for n=4:
%e A207656 ..1..0..1....1..0..0....1..0..0....1..1..0....0..0..1....0..1..1....1..0..1
%e A207656 ..1..0..1....0..1..1....0..0..1....1..1..0....0..1..1....1..0..0....0..1..1
%e A207656 ..1..0..1....1..0..0....1..0..1....0..1..0....0..1..1....0..1..1....1..0..0
%e A207656 ..0..0..1....0..1..1....0..0..1....1..1..0....0..0..1....1..0..1....0..1..1
%Y A207656 Cf. A207661.
%K A207656 nonn
%O A207656 1,1
%A A207656 _R. H. Hardin_, Feb 19 2012