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A228502 Number of n X 4 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally. 1

%I #12 Sep 12 2018 06:13:29

%S 3,5,29,87,358,1252,4749,17285,64235,236211,873250,3219652,11886927,

%T 43856285,161862005,597285195,2204231074,8134165648,30017792409,

%U 110774426621,408792375587,1508567655759,5567079710158,20544224979592

%N Number of n X 4 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.

%H R. H. Hardin, <a href="/A228502/b228502.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 7*a(n-2) - 2*a(n-3) - 3*a(n-4).

%F Empirical g.f.: x*(1 - x)*(3 + 2*x) / (1 - 2*x - 7*x^2 + 2*x^3 + 3*x^4). - _Colin Barker_, Sep 12 2018

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A228506.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 23 2013

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