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A184047 1/9 the number of (n+1) X 9 0..2 arrays with all 2 X 2 subblocks having the same four values.

%I A184047 #8 Apr 10 2018 14:16:50
%S A184047 561,567,577,597,633,705,841,1113,1641,2697,4777,8937,17193,33705,
%T A184047 66601,132393,263721,526377,1051177,2100777,4198953,8395305,16785961,
%U A184047 33567273,67125801,134242857,268468777,536920617,1073807913,2147582505,4295098921
%N A184047 1/9 the number of (n+1) X 9 0..2 arrays with all 2 X 2 subblocks having the same four values.
%C A184047 Column 8 of A184048.
%H A184047 R. H. Hardin, <a href="/A184047/b184047.txt">Table of n, a(n) for n = 1..158</a>
%F A184047 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184047 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184047 G.f.: x*(561 - 1116*x - 1124*x^2 + 2232*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184047 a(n) = 3*2^(n/2) + 2^(n+1) + 553 for n even.
%F A184047 a(n) = 2^(n+1) + 2^((n+3)/2) + 553 for n odd.
%F A184047 (End)
%e A184047 Some solutions for 5 X 9:
%e A184047 ..2..0..2..0..0..1..0..1..2....1..1..0..0..0..0..1..0..1
%e A184047 ..0..1..0..1..2..0..2..0..0....0..0..1..1..1..1..0..1..0
%e A184047 ..2..0..2..0..0..1..0..1..2....1..1..0..0..0..0..1..0..1
%e A184047 ..0..1..0..1..2..0..2..0..0....0..0..1..1..1..1..0..1..0
%e A184047 ..2..0..2..0..0..1..0..1..2....1..1..0..0..0..0..1..0..1
%Y A184047 Cf. A184048.
%K A184047 nonn
%O A184047 1,1
%A A184047 _R. H. Hardin_, Jan 08 2011