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Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.
1

%I #10 Sep 01 2013 17:50:07

%S 2,4,14,41,127,386,1181,3605,11013,33635,102734,313780,958385,2927208,

%T 8940618,27307464,83405606,254747013,778077691,2376494562,7258563605,

%U 22169941573,67713990833,206819875427,631693101322,1929389878184

%N Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.

%C Column 3 of A228482

%C Same recurrences as A228285 except in addition a smaller one for column 5

%H R. H. Hardin, <a href="/A228477/b228477.txt">Table of n, a(n) for n = 1..210</a>

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

%F G.f.: -x*(-2-2*x+x^3) / ( (1+x)*(x^4-x^3-3*x^2-2*x+1) ). - _R. J. Mathar_, Aug 25 2013

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Aug 22 2013