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A184043 1/9 the number of (n+1) X 5 0..2 arrays with all 2 X 2 subblocks having the same four values.

%I A184043 #8 Apr 10 2018 11:52:09
%S A184043 45,51,61,81,117,189,325,597,1125,2181,4261,8421,16677,33189,66085,
%T A184043 131877,263205,525861,1050661,2100261,4198437,8394789,16785445,
%U A184043 33566757,67125285,134242341,268468261,536920101,1073807397,2147581989,4295098405
%N A184043 1/9 the number of (n+1) X 5 0..2 arrays with all 2 X 2 subblocks having the same four values.
%C A184043 Column 4 of A184048.
%H A184043 R. H. Hardin, <a href="/A184043/b184043.txt">Table of n, a(n) for n = 1..200</a>
%F A184043 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184043 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184043 G.f.: x*(45 - 84*x - 92*x^2 + 168*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184043 a(n) = 3*2^(n/2) + 2^(n+1) + 37 for n even.
%F A184043 a(n) = 2^(n+1) + 2^((n+3)/2) + 37 for n odd.
%F A184043 (End)
%e A184043 Some solutions for 7 X 5:
%e A184043 ..0..1..0..1..0....2..0..2..0..2....1..2..1..2..1....0..0..0..1..0
%e A184043 ..0..1..0..1..0....2..2..2..2..2....0..0..0..0..0....1..1..1..0..1
%e A184043 ..1..0..1..0..1....0..2..0..2..0....1..2..1..2..1....0..0..0..1..0
%e A184043 ..0..1..0..1..0....2..2..2..2..2....0..0..0..0..0....1..1..1..0..1
%e A184043 ..0..1..0..1..0....0..2..0..2..0....2..1..2..1..2....0..0..0..1..0
%e A184043 ..0..1..0..1..0....2..2..2..2..2....0..0..0..0..0....1..1..1..0..1
%e A184043 ..1..0..1..0..1....2..0..2..0..2....2..1..2..1..2....0..0..0..1..0
%Y A184043 Cf. A184048.
%K A184043 nonn
%O A184043 1,1
%A A184043 _R. H. Hardin_, Jan 08 2011