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A206687 Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.

%I A206687 #8 Feb 23 2018 08:35:39
%S A206687 1,4,11,36,116,376,1216,3936,12736,41216,133376,431616,1396736,
%T A206687 4519936,14626816,47333376,153174016,495681536,1604059136,5190844416,
%U A206687 16797925376,54359228416,175910158336,569257230336,1842155094016,5961339109376
%N A206687 Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
%C A206687 Column 2 of A206692.
%H A206687 R. H. Hardin, <a href="/A206687/b206687.txt">Table of n, a(n) for n = 1..210</a>
%F A206687 Empirical: a(n) = 2*a(n-1) + 4*a(n-2) for n>4.
%F A206687 Conjectures from _Colin Barker_, Feb 23 2018: (Start)
%F A206687 G.f.: x*(1 - x)*(1 + x)*(1 + 2*x) / (1 - 2*x - 4*x^2).
%F A206687 a(n) = ((1-sqrt(5))^n*(-5+3*sqrt(5)) + (1+sqrt(5))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>2.
%F A206687 (End)
%e A206687 All solutions for n=4:
%e A206687 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A206687 ..2..3....1..0....2..3....1..0....2..3....1..2....1..2....1..2....1..0
%e A206687 ..1..2....2..3....1..0....2..3....3..2....2..0....3..0....2..3....2..3
%e A206687 ..0..1....3..2....3..1....3..1....1..0....3..1....0..1....0..1....0..1
%Y A206687 Cf. A206692.
%K A206687 nonn
%O A206687 1,2
%A A206687 _R. H. Hardin_, Feb 11 2012