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%I #8 May 29 2018 08:29:06
%S 338,574,1102,1890,3122,4822,7238,10394,14602,19886,26622,34834,44962,
%T 57030,71542,88522,108538,131614,158382,188866,223762,263094,307622,
%U 357370,413162,475022,543838,619634,703362,795046,895702,1005354,1125082
%N Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.
%C Column 4 of A202447.
%H R. H. Hardin, <a href="/A202443/b202443.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7) for n>8.
%F Conjectures from _Colin Barker_, May 29 2018: (Start)
%F G.f.: 2*x*(169 - 220*x - 141*x^2 + 424*x^3 - 133*x^4 - 176*x^5 + 137*x^6 - 28*x^7) / ((1 - x)^5*(1 + x)^2).
%F a(n) = (2/3)*(n^4 + 12*n^3 + 59*n^2 + 177*n + 159) for n even.
%F a(n) = (2/3)*(n^4 + 12*n^3 + 59*n^2 + 183*n + 168) for n>1 and odd.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0..0..0....1..0..1..1..1..1....1..1..1..1..1..1....1..0..1..0..1..1
%e ..0..1..1..1..1..1....1..0..0..0..0..0....1..0..1..0..0..0....1..0..1..0..0..0
%e ..0..1..0..0..0..0....1..0..1..0..1..1....1..0..1..1..1..1....1..0..1..0..1..0
%e ..0..1..0..1..1..1....1..0..0..0..0..0....1..0..1..0..1..1....1..0..1..0..0..0
%e ..0..1..0..1..0..1....1..0..1..0..1..0....1..0..1..1..1..1....1..0..1..0..1..0
%e ..0..1..0..1..1..1....1..0..1..0..0..0....1..0..1..1..1..1....1..0..1..0..0..0
%Y Cf. A202447.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2011