%I
%S 34,94,265,739,2059,5746,16033,44728,124786,348145,971293,2709817,
%T 7560148,21092137,58845166,164172730,458027185,1277854735,3565100011,
%U 9946309042,27749309485,77418082780,215989502182,602591324641
%N Number of (n+2) X 3 binary arrays with no more than one of any consecutive three bits set in any row or column.
%C Column 1 of A202421.
%H R. H. Hardin, <a href="/A202414/b202414.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n1) +a(n2) +3*a(n3) +a(n4).
%F Empirical g.f.: x*(34 + 26*x + 43*x^2 + 13*x^3) / (1  2*x  x^2  3*x^3  x^4).  _Colin Barker_, May 28 2018
%e Some solutions for n=5:
%e ..0..1..0....0..0..0....1..0..0....0..0..1....0..0..0....0..0..1....0..0..1
%e ..1..0..0....0..0..1....0..1..0....1..0..0....0..0..1....0..0..0....0..0..0
%e ..0..0..0....1..0..0....0..0..0....0..0..0....0..1..0....1..0..0....1..0..0
%e ..0..0..1....0..0..0....1..0..0....0..0..1....0..0..0....0..0..0....0..0..0
%e ..0..1..0....0..1..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0
%e ..0..0..0....0..0..0....0..0..1....0..0..0....0..1..0....1..0..0....0..1..0
%e ..1..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....1..0..0
%Y Cf. A202421.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2011
