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A208064 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

%I A208064 #8 Jun 27 2018 05:50:17
%S A208064 6,36,72,144,216,324,432,576,720,900,1080,1296,1512,1764,2016,2304,
%T A208064 2592,2916,3240,3600,3960,4356,4752,5184,5616,6084,6552,7056,7560,
%U A208064 8100,8640,9216,9792,10404,11016,11664,12312,12996,13680,14400,15120,15876,16632
%N A208064 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
%C A208064 Column 3 of A208069.
%H A208064 R. H. Hardin, <a href="/A208064/b208064.txt">Table of n, a(n) for n = 1..210</a>
%F A208064 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5.
%F A208064 Conjectures from _Colin Barker_, Jun 27 2018: (Start)
%F A208064 G.f.: 6*x*(1 + 4*x + 2*x^3 - x^4) / ((1 - x)^3*(1 + x)).
%F A208064 a(n) = 9*n^2 for n>1 and even.
%F A208064 a(n) = 9*n^2-9 for n>1 and odd.
%F A208064 (End)
%e A208064 Some solutions for n=4:
%e A208064 ..0..0..1....1..1..0....1..1..0....0..1..1....1..1..0....0..0..1....0..0..1
%e A208064 ..0..1..1....1..0..1....1..1..0....1..1..0....0..0..1....0..1..1....0..0..1
%e A208064 ..0..0..1....1..0..0....1..0..0....0..1..1....1..1..0....0..0..1....0..0..1
%e A208064 ..0..0..1....0..0..1....1..1..0....1..0..0....0..0..1....0..1..0....0..0..1
%Y A208064 Cf. A208069.
%K A208064 nonn
%O A208064 1,1
%A A208064 _R. H. Hardin_, Feb 23 2012