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%I #8 Jul 02 2018 04:53:43
%S 2,13,113,982,8534,74164,644516,5601112,48675992,423014608,3676172816,
%T 31947470176,277636798304,2412779207488,20968054449728,
%U 182221110842752,1583577213440384,13761944372579584,119597018261278976
%N Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.
%C Column 2 of A208322.
%H R. H. Hardin, <a href="/A208316/b208316.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) + 6*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Jul 02 2018: (Start)
%F G.f.: x*(2 - 3*x - 3*x^2) / (1 - 8*x - 6*x^2).
%F a(n) = ((4-sqrt(22))^n*(-5+sqrt(22)) + (4+sqrt(22))^n*(5+sqrt(22))) / (12*sqrt(22)) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0
%e ..0..1....0..1....1..1....0..1....0..1....1..1....1..1....0..1....0..2....1..2
%e ..1..0....2..0....0..0....0..1....2..1....2..0....1..2....0..0....1..2....0..2
%e ..1..2....1..0....2..0....2..0....0..2....0..1....1..1....2..1....2..1....2..0
%Y Cf. A208322.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 25 2012
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