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Number of n X 2 arrays of occupancy after each element moves to some king-move neighbor, with every occupancy equal to zero or two.
2

%I #10 Mar 14 2018 11:20:22

%S 0,6,16,52,174,588,1984,6688,22536,75924,255760,861496,2901696,

%T 9773184,32916280,110861104,373373568,1257492096,4235114944,

%U 14263430416,48037679232,161785483872,544874848384,1835074738624,6180315022560

%N Number of n X 2 arrays of occupancy after each element moves to some king-move neighbor, with every occupancy equal to zero or two.

%C Column 2 of A221273.

%H R. H. Hardin, <a href="/A221270/b221270.txt">Table of n, a(n) for n = 1..65</a>

%F Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3) - 2*a(n-5).

%F Empirical g.f.: 2*x^2*(1 - x)*(3 - 7*x + x^2) / (1 - 6*x + 10*x^2 - 4*x^3 + 2*x^5). - _Colin Barker_, Mar 14 2018

%e Some solutions for n=4:

%e ..0..2....0..0....0..2....2..0....0..2....2..0....0..0....0..2....2..2....0..0

%e ..2..2....0..2....2..0....2..0....0..2....0..2....2..2....0..2....0..0....2..2

%e ..0..2....2..0....2..0....0..2....0..2....2..0....0..2....0..0....0..0....2..0

%e ..0..0....2..2....2..0....2..0....0..2....0..2....2..0....2..2....2..2....2..0

%Y Cf. A221273.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 08 2013