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Number of n X 4 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
1

%I #12 Sep 13 2018 06:07:48

%S 3,16,97,586,3588,22060,135768,835776,5145232,31675616,195005248,

%T 1200515520,7390763648,45499943936,280112449792,1724463325696,

%U 10616356983808,65357745761280,402363535587328,2477080763498496

%N Number of n X 4 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.

%H R. H. Hardin, <a href="/A228792/b228792.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 12*a(n-2) + 4*a(n-3) for n>4.

%F Empirical g.f.: x*(3 - 8*x + 5*x^2 - 10*x^3) / (1 - 8*x + 12*x^2 - 4*x^3). - _Colin Barker_, Sep 13 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A228796.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 04 2013