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Number of n X 2 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, with every occupancy equal to zero or two.
1

%I #9 Aug 05 2018 08:21:57

%S 0,5,10,31,90,259,746,2150,6192,17831,51346,147850,425724,1225834,

%T 3529664,10163285,29264046,84262511,242624302,698608939,2011564422,

%U 5792069134,16677598712,48021232079,138271627638,398137284986

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

%C Column 2 of A221308.

%H R. H. Hardin, <a href="/A221304/b221304.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(5 - 10*x + 6*x^2 - 4*x^3 + 2*x^4) / ((1 - 3*x + x^3)*(1 - x - x^3)). - _Colin Barker_, Aug 05 2018

%e All solutions for n=3:

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

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

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

%Y Cf. A221308.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 09 2013