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A184041 1/9 the number of (n+1) X 3 0..2 arrays with all 2 X 2 subblocks having the same four values.

%I A184041 #8 Apr 10 2018 08:32:19
%S A184041 15,21,31,51,87,159,295,567,1095,2151,4231,8391,16647,33159,66055,
%T A184041 131847,263175,525831,1050631,2100231,4198407,8394759,16785415,
%U A184041 33566727,67125255,134242311,268468231,536920071,1073807367,2147581959,4295098375
%N A184041 1/9 the number of (n+1) X 3 0..2 arrays with all 2 X 2 subblocks having the same four values.
%C A184041 Column 2 of A184048.
%H A184041 R. H. Hardin, <a href="/A184041/b184041.txt">Table of n, a(n) for n = 1..200</a>
%F A184041 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184041 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184041 G.f.: x*(15 - 24*x - 32*x^2 + 48*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184041 a(n) = 3*2^(n/2) + 2^(n+1) + 7 for n even.
%F A184041 a(n) = 2^(n+1) + 2^((n+3)/2) + 7 for n odd.
%F A184041 (End)
%e A184041 Some solutions for 5 X 3:
%e A184041 ..1..0..0....2..1..2....2..1..2....0..1..0....0..0..0....0..1..0....1..1..1
%e A184041 ..0..1..1....0..0..0....1..1..1....0..2..0....1..1..1....1..2..1....0..1..0
%e A184041 ..1..0..0....2..1..2....2..1..2....1..0..1....0..0..0....1..0..1....1..1..1
%e A184041 ..0..1..1....0..0..0....1..1..1....0..2..0....1..1..1....2..1..2....0..1..0
%e A184041 ..1..0..0....1..2..1....1..2..1....1..0..1....0..0..0....0..1..0....1..1..1
%Y A184041 Cf. A184048.
%K A184041 nonn
%O A184041 1,1
%A A184041 _R. H. Hardin_, Jan 08 2011