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A184044 1/9 the number of (n+1) X 6 0..2 arrays with all 2 X 2 subblocks having the same four values.

%I A184044 #12 Aug 01 2025 17:05:42
%S A184044 81,87,97,117,153,225,361,633,1161,2217,4297,8457,16713,33225,66121,
%T A184044 131913,263241,525897,1050697,2100297,4198473,8394825,16785481,
%U A184044 33566793,67125321,134242377,268468297,536920137,1073807433,2147582025,4295098441,8590131273,17180131401
%N A184044 1/9 the number of (n+1) X 6 0..2 arrays with all 2 X 2 subblocks having the same four values.
%H A184044 R. H. Hardin, <a href="/A184044/b184044.txt">Table of n, a(n) for n = 1..200</a>
%F A184044 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184044 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184044 G.f.: x*(81 - 156*x - 164*x^2 + 312*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184044 a(n) = 3*2^(n/2) + 2^(n+1) + 73 for n even.
%F A184044 a(n) = 2^(n+1) + 2^((n+3)/2) + 73 for n odd. (End)
%F A184044 Conjectured e.g.f.: 2*cosh(2*x) + 3*cosh(sqrt(2)*x) + 73*sinh(x) + cosh(x)*(73 + 4*sinh(x)) + 2*sqrt(2)*sinh(sqrt(2)*x) - 78. - _Stefano Spezia_, Aug 01 2025
%e A184044 Some solutions for 5 X 6:
%e A184044 ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0
%e A184044 ..1..1..2..1..1..0....2..0..2..1..2..1....1..0..0..2..0..2....2..0..2..2..2..2
%e A184044 ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0
%e A184044 ..1..1..2..1..1..0....2..0..2..1..2..1....1..0..0..2..0..2....2..0..2..2..2..2
%e A184044 ..2..0..1..0..2..1....2..1..2..0..2..0....0..2..1..0..1..0....1..2..1..0..1..0
%Y A184044 Column 5 of A184048.
%K A184044 nonn
%O A184044 1,1
%A A184044 _R. H. Hardin_, Jan 08 2011