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%I #11 Oct 13 2018 09:22:28
%S 32,80,192,512,1280,3584,9216,26624,69632,204800,540672,1605632,
%T 4259840,12713984,33816576,101187584,269484032,807403520,2151677952,
%U 6450839552,17196646400,51573161984,137506062336,412451078144,1099780063232
%N Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
%H R. H. Hardin, <a href="/A234133/b234133.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3).
%F Conjectures from _Colin Barker_, Oct 13 2018: (Start)
%F G.f.: 16*x*(2 + x - 14*x^2) / ((1 - 2*x)*(1 - 8*x^2)).
%F a(n) = 2^(3+n) + 2^(-1/2+(3*n)/2)*(4-4*(-1)^n + 3*sqrt(2) + 3*(-1)^n*sqrt(2)).
%F (End)
%e Some solutions for n=5:
%e 3 3 0 0 0 3 3 1 3 0 1 1 0 0 3 0 3 0 3 2
%e 0 3 0 3 3 3 0 1 3 3 0 3 3 0 3 3 0 0 0 2
%e 1 1 0 0 0 3 1 3 0 3 0 0 1 1 3 0 3 0 2 3
%e 0 3 0 3 0 0 0 1 3 3 3 0 0 3 0 0 0 0 0 2
%e 2 2 2 2 0 3 3 1 0 3 1 1 2 2 0 3 3 0 2 3
%e 0 3 0 3 0 0 0 1 3 3 3 0 0 3 2 2 1 1 2 0
%Y Column 1 of A234140.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2013
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