%I #8 Jun 04 2018 05:47:19
%S 3,30,206,1570,11541,85932,636912,4728287,35081894,260344178,
%T 1931891935,14336007171,106382441959,789428803920,5858083254752,
%U 43470863287881,322582598884187,2393776652484473,17763408799398613,131816263437678307
%N Number of n X 3 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by both a 1 and a 0.
%C Column 3 of A203371.
%H R. H. Hardin, <a href="/A203366/b203366.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +26*a(n-2) +44*a(n-3) +45*a(n-4) +24*a(n-5) -a(n-6) -17*a(n-7) +2*a(n-8) -2*a(n-9).
%F Empirical g.f.: x*(3 + 21*x + 38*x^2 + 40*x^3 + 20*x^4 + 3*x^5 - 17*x^6 + 2*x^7 - 2*x^8) / (1 - 3*x - 26*x^2 - 44*x^3 - 45*x^4 - 24*x^5 + x^6 + 17*x^7 - 2*x^8 + 2*x^9). - _Colin Barker_, Jun 04 2018
%e Some solutions for n=4:
%e ..0..1..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..0..1
%e ..1..0..1....0..0..1....0..0..2....0..1..2....1..1..1....1..2..1....0..0..2
%e ..0..1..0....1..2..0....1..0..0....0..2..0....0..0..0....0..0..2....1..1..0
%e ..0..1..2....0..0..1....0..0..1....0..1..1....1..2..0....0..0..0....0..0..1
%Y Cf. A203371.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 31 2011