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%I #13 Mar 03 2018 05:35:45
%S 108,240,450,756,1176,1728,2430,3300,4356,5616,7098,8820,10800,13056,
%T 15606,18468,21660,25200,29106,33396,38088,43200,48750,54756,61236,
%U 68208,75690,83700,92256,101376,111078,121380,132300,143856,156066,168948
%N Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C Column 1 of A202202.
%H R. H. Hardin, <a href="/A202195/b202195.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*(n+3)*(n+2)^2 = 3*A011379(n+2).
%F Conjectures from _Colin Barker_, Mar 03 2018: (Start)
%F G.f.: 6*x*(18 - 32*x + 23*x^2 - 6*x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=10:
%e 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1
%e 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1
%e 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1
%e 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1
%e 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1
%e 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0
%e 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0
%e 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0
%e 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
%e 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
%e 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%Y Cf. A202202.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 14 2011
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