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A184038 1/16 the number of (n+1) X 9 0..3 arrays with all 2 X 2 subblocks having the same four values.

%I A184038 #8 Apr 10 2018 06:28:00
%S A184038 1225,1237,1258,1300,1378,1534,1834,2434,3610,5962,10618,19930,38458,
%T A184038 75514,149434,297274,592570,1183162,2363578,4724410,9444538,18884794,
%U A184038 37762234,75517114,151020730,302027962,604030138,1208034490,2416018618
%N A184038 1/16 the number of (n+1) X 9 0..3 arrays with all 2 X 2 subblocks having the same four values.
%C A184038 Column 8 of A184039.
%H A184038 R. H. Hardin, <a href="/A184038/b184038.txt">Table of n, a(n) for n = 1..53</a>
%F A184038 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184038 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184038 G.f.: x*(1225 - 2438*x - 2453*x^2 + 4876*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184038 a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 1210 for n even.
%F A184038 a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 1210 for n odd.
%F A184038 (End)
%e A184038 Some solutions for 3 X 9:
%e A184038 ..3..0..3..1..3..0..3..1..3....0..0..3..1..3..1..0..0..0
%e A184038 ..1..1..1..0..1..1..1..0..1....3..1..0..0..0..0..3..1..3
%e A184038 ..3..0..3..1..3..0..3..1..3....0..0..3..1..3..1..0..0..0
%K A184038 nonn
%O A184038 1,1
%A A184038 _R. H. Hardin_, Jan 08 2011