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%I #9 Feb 14 2018 11:10:37
%S 96,260,804,2554,8372,27649,91973,306486,1023025,3416176,11412046,
%T 38126620,127389228,425644289,1422231173,4752212465,15879019404,
%U 53058142574,177288642743,592392993030,1979424904812,6614060706429
%N Number of (n+2) X 3 binary arrays avoiding patterns 001 and 100 in rows, columns and nw-to-se diagonals.
%C Column 1 of A202591.
%H R. H. Hardin, <a href="/A202584/b202584.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +5*a(n-2) -11*a(n-3) -10*a(n-4) +9*a(n-5) +12*a(n-6) -2*a(n-7) -6*a(n-8) +a(n-10).
%F Empirical g.f.: x*(96 - 28*x - 456*x^2 - 102*x^3 + 510*x^4 + 343*x^5 - 192*x^6 - 210*x^7 + 23*x^8 + 36*x^9) / ((1 - x)*(1 + x - x^2)*(1 - x - x^2)*(1 - 2*x - 4*x^2 - 2*x^3 + x^4 + x^5)). - _Colin Barker_, Feb 14 2018
%e Some solutions for n=3:
%e ..1..1..0....1..1..1....1..1..1....1..1..0....0..1..0....1..0..1....0..1..0
%e ..1..1..1....1..1..1....0..1..1....1..1..1....0..1..0....0..1..0....1..1..1
%e ..0..0..0....1..0..1....1..1..1....0..1..1....0..0..0....1..0..1....0..1..1
%e ..1..1..1....1..1..1....0..1..1....1..1..1....0..1..0....1..1..0....1..1..1
%e ..1..1..1....0..1..0....1..0..1....1..1..0....0..0..0....1..0..1....0..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 21 2011
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