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%I #8 Apr 19 2018 05:59:59
%S 126,606,2904,14229,70767,351549,1750896,8730234,43522407,217032372,
%T 1082345247,5397586308,26918218566,134243793585,669486128850,
%U 3338798653422,16650942997338,83040015704427,414129463721703
%N Half the number of (n+2) X 3 binary arrays with each 3 X 3 subblock having sum 4 or 5.
%C Column 1 of A186825.
%H R. H. Hardin, <a href="/A186817/b186817.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) + 9*a(n-2) + 15*a(n-3) - 36*a(n-4) - 72*a(n-5) - 27*a(n-6) - 81*a(n-7).
%F Empirical g.f.: 3*x*(42 + 76*x - 16*x^2 - 609*x^3 - 870*x^4 - 495*x^5 - 837*x^6) / (1 - 3*x - 9*x^2 - 15*x^3 + 36*x^4 + 72*x^5 + 27*x^6 + 81*x^7). - _Colin Barker_, Apr 19 2018
%e Some solutions for 4 X 3 with a(1,1)=0:
%e ..0..1..0....0..1..0....0..1..0....0..0..1....0..0..1....0..1..0....0..0..1
%e ..0..0..1....0..1..1....1..0..1....1..1..1....1..0..0....1..0..1....0..1..1
%e ..0..1..1....0..1..0....0..0..1....0..0..0....0..1..1....0..1..1....0..1..0
%e ..0..0..1....1..0..0....0..0..1....1..0..0....0..1..0....1..0..0....1..0..1
%Y Cf. A186825.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 27 2011