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A184032 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values.

%I A184032 #8 Apr 10 2018 04:52:31
%S A184032 28,40,61,103,181,337,637,1237,2413,4765,9421,18733,37261,74317,
%T A184032 148237,296077,591373,1181965,2362381,4723213,9443341,18883597,
%U A184032 37761037,75515917,151019533,302026765,604028941,1208033293,2416017421,4831985677
%N A184032 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values.
%C A184032 Column 2 of A184039.
%H A184032 R. H. Hardin, <a href="/A184032/b184032.txt">Table of n, a(n) for n = 1..200</a>
%F A184032 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184032 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184032 G.f.: x*(28 - 44*x - 59*x^2 + 88*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184032 a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 13 for n even.
%F A184032 a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 13 for n odd.
%F A184032 (End)
%e A184032 Some solutions for 5 X 3:
%e A184032 ..1..2..1....0..1..0....0..1..0....1..3..1....2..1..2....3..2..3....3..2..3
%e A184032 ..0..1..0....2..3..2....1..0..1....1..0..1....3..0..3....0..3..0....2..3..2
%e A184032 ..2..1..2....0..1..0....0..1..0....3..1..3....2..1..2....3..2..3....2..3..2
%e A184032 ..0..1..0....3..2..3....0..1..0....0..1..0....3..0..3....3..0..3....2..3..2
%e A184032 ..2..1..2....1..0..1....0..1..0....1..3..1....1..2..1....2..3..2....2..3..2
%Y A184032 Cf. A184039.
%K A184032 nonn
%O A184032 1,1
%A A184032 _R. H. Hardin_, Jan 08 2011