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%I #8 Aug 10 2018 09:17:20
%S 3,35,396,4429,49387,550264,6129659,68277335,760519092,8471140593,
%T 94356794511,1051003927840,11706726309807,130396694392883,
%U 1452438312980628,16178148223958949,180202131485051219
%N Number of n X 2 arrays of occupancy after each element stays put or moves to some king-move neighbor, without consecutive moves in the same direction.
%C Column 2 of A221688.
%H R. H. Hardin, <a href="/A221687/b221687.txt">Table of n, a(n) for n = 1..23</a>
%F Empirical: a(n) = 13*a(n-1) - 18*a(n-2) - 29*a(n-3) - 15*a(n-4) - 12*a(n-5) - 2*a(n-6).
%F Empirical g.f.: x*(3 - 4*x - 5*x^2 - 2*x^3 - 2*x^4) / (1 - 13*x + 18*x^2 + 29*x^3 + 15*x^4 + 12*x^5 + 2*x^6). - _Colin Barker_, Aug 10 2018
%e Some solutions for n=3:
%e ..0..0....2..0....0..0....0..1....0..0....1..1....0..0....0..1....1..1....2..0
%e ..2..4....1..2....3..2....3..1....3..2....2..0....6..0....2..2....2..0....0..4
%e ..0..0....0..1....0..1....0..1....1..0....0..2....0..0....0..1....2..0....0..0
%Y Cf. A221688.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 22 2013
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