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Half the number of n X 3 binary arrays with no 1 having an adjacent 1 both above and to its left.
1

%I #9 Apr 14 2018 13:11:22

%S 4,25,163,1056,6847,44391,287802,1865917,12097367,78431296,508496451,

%T 3296753387,21373960178,138574567177,898425491035,5824794400480,

%U 37764099690423,244837350020575,1587362824918602,10291406673539877

%N Half the number of n X 3 binary arrays with no 1 having an adjacent 1 both above and to its left.

%C Column 3 of A184761.

%H R. H. Hardin, <a href="/A184755/b184755.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) + 9*a(n-2) + 4*a(n-3).

%F Empirical g.f.: x*(4 + 5*x + 2*x^2) / (1 - 5*x - 9*x^2 - 4*x^3). - _Colin Barker_, Apr 14 2018

%e Some solutions for 5 X 3:

%e ..0..1..0....1..0..1....1..1..0....1..0..0....0..0..0....0..1..1....1..1..0

%e ..0..1..0....1..0..1....1..0..0....0..1..0....1..1..1....1..0..0....1..0..1

%e ..0..1..0....1..0..1....0..1..0....0..0..1....1..0..0....0..1..1....0..1..0

%e ..0..1..0....1..0..1....0..1..0....0..0..0....1..0..0....1..0..0....0..0..0

%e ..0..0..0....1..0..0....1..0..0....0..1..0....1..1..1....1..0..1....1..1..0

%Y Cf. A184761.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 21 2011