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A184034 1/16 the number of (n+1) X 5 0..3 arrays with all 2 X 2 subblocks having the same four values.

%I A184034 #8 Apr 10 2018 05:25:21
%S A184034 91,103,124,166,244,400,700,1300,2476,4828,9484,18796,37324,74380,
%T A184034 148300,296140,591436,1182028,2362444,4723276,9443404,18883660,
%U A184034 37761100,75515980,151019596,302026828,604029004,1208033356,2416017484,4831985740
%N A184034 1/16 the number of (n+1) X 5 0..3 arrays with all 2 X 2 subblocks having the same four values.
%C A184034 Column 4 of A184039.
%H A184034 R. H. Hardin, <a href="/A184034/b184034.txt">Table of n, a(n) for n = 1..200</a>
%F A184034 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184034 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184034 G.f.: x*(91 - 170*x - 185*x^2 + 340*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184034 a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 76 for n even.
%F A184034 a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 76 for n odd.
%F A184034 (End)
%e A184034 Some solutions for 3 X 5:
%e A184034 ..3..1..0..1..3....2..3..3..3..3....2..1..2..0..2....1..1..3..2..1
%e A184034 ..0..2..3..2..0....3..0..2..0..2....3..0..3..1..3....3..2..1..1..3
%e A184034 ..3..1..0..1..3....2..3..3..3..3....2..1..2..0..2....1..1..3..2..1
%Y A184034 Cf. A184039.
%K A184034 nonn
%O A184034 1,1
%A A184034 _R. H. Hardin_, Jan 08 2011