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%I #10 May 28 2018 18:25:55
%S 80,138,224,338,484,666,888,1154,1468,1834,2256,2738,3284,3898,4584,
%T 5346,6188,7114,8128,9234,10436,11738,13144,14658,16284,18026,19888,
%U 21874,23988,26234,28616,31138,33804,36618,39584,42706,45988,49434,53048,56834
%N Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.
%C Column 1 of A202447.
%H R. H. Hardin, <a href="/A202440/b202440.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/3)*n^3 + 8*n^2 + (100/3)*n + 34 for n>1.
%F Conjectures from _Colin Barker_, May 28 2018: (Start)
%F G.f.: 2*x*(40 - 91*x + 76*x^2 - 25*x^3 + 2*x^4) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F (End)
%e Some solutions for n=4:
%e 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0
%e 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1
%e 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0
%e 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0
%e 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0
%e 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0
%Y Cf. A202447.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2011
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