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A208428 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

%I A208428 #10 Jun 29 2023 13:14:31
%S A208428 2,14,54,216,864,3456,13824,55296,221184,884736,3538944,14155776,
%T A208428 56623104,226492416,905969664,3623878656,14495514624,57982058496,
%U A208428 231928233984,927712935936,3710851743744,14843406974976,59373627899904
%N A208428 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
%C A208428 Column 2 of A208434.
%H A208428 R. H. Hardin, <a href="/A208428/b208428.txt">Table of n, a(n) for n = 1..210</a>
%H A208428 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (4).
%F A208428 Empirical: a(n) = 4*a(n-1) for n>3.
%F A208428 Conjectures from _Colin Barker_, Feb 23 2018: (Start)
%F A208428 G.f.: 2*x*(1 + 3*x - x^2) / (1 - 4*x).
%F A208428 a(n) = 27*2^(2*n - 5) for n>2.
%F A208428 (End)
%e A208428 Some solutions for n=4:
%e A208428 ..0..0....0..0....0..0....0..1....0..0....0..0....0..1....0..0....0..0....0..0
%e A208428 ..1..1....0..0....1..1....2..1....1..2....0..0....0..2....0..1....1..1....0..0
%e A208428 ..1..1....1..2....1..2....2..1....1..2....1..2....2..2....2..1....2..1....1..1
%e A208428 ..2..0....1..2....2..2....0..1....0..0....2..2....0..1....2..1....0..2....1..1
%Y A208428 Cf. A208434.
%K A208428 nonn
%O A208428 1,1
%A A208428 _R. H. Hardin_, Feb 26 2012