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%I #8 Jun 01 2018 11:24:17
%S 66,172,462,1278,3448,9394,25526,69336,188418,511960,1391014,3779620,
%T 10269688,27904004,75818836,206009414,559753846,1520922896,4132541760,
%U 11228644088,30509661310,82898648850,225246223922,612022778622
%N Number of (n+2) X 3 binary arrays avoiding patterns 000 and 111 in rows, columns and nw-to-se diagonals.
%C Column 1 of A202647.
%H R. H. Hardin, <a href="/A202640/b202640.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -5*a(n-4) -2*a(n-5) +5*a(n-6) +a(n-7) -2*a(n-8) for n>9.
%F Empirical g.f.: 2*x*(33 + 20*x - 40*x^2 - 48*x^3 + 4*x^4 + 59*x^5 - 2*x^6 - 31*x^7 + 4*x^8) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - x^3 + 3*x^4 + x^5 - 2*x^6)). - _Colin Barker_, Jun 01 2018
%e Some solutions for n=3:
%e ..1..0..1....0..1..0....1..0..1....1..0..0....1..0..1....0..1..0....1..1..0
%e ..0..1..1....1..0..0....0..1..0....1..0..0....0..1..1....1..0..1....0..0..1
%e ..0..1..0....0..1..1....0..1..0....0..1..1....1..1..0....0..0..1....0..1..0
%e ..1..0..0....1..0..0....1..0..1....0..1..0....0..0..1....0..1..0....1..0..0
%e ..1..0..1....1..0..1....0..1..1....1..0..0....0..0..1....1..0..1....0..0..1
%Y Cf. A202647.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2011
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