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Number of (n+1) X (3+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.
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%I #11 Oct 13 2018 11:53:25

%S 192,296,488,968,1992,4808,11336,30536,76872,218696,567368,1657928,

%T 4362312,12916808,34218056,101986376,271073352,810573896,2158002248,

%U 6463471688,17221877832,51623592008,137606856776,412652601416

%N Number of (n+1) X (3+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="/A234135/b234135.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 8*a(n-2) - 30*a(n-3) + 4*a(n-4) + 48*a(n-5) - 32*a(n-6).

%F Empirical g.f.: 8*x*(24 - 35*x - 242*x^2 + 362*x^3 + 412*x^4 - 584*x^5) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)*(1 - 8*x^2)). - _Colin Barker_, Oct 13 2018

%e Some solutions for n=5:

%e 3 0 3 0 0 1 0 1 0 3 0 0 1 1 1 1 3 3 3 3

%e 2 2 2 2 1 3 1 3 3 3 3 0 3 0 3 0 3 0 3 0

%e 0 3 0 3 0 1 0 1 3 0 3 3 2 2 2 2 1 1 1 1

%e 3 3 3 3 3 1 3 1 0 0 0 3 3 0 3 0 3 0 3 0

%e 0 3 0 3 0 1 0 1 3 0 3 3 1 1 1 1 0 0 0 0

%e 2 2 2 2 3 1 3 1 3 3 3 0 3 0 3 0 3 0 3 0

%Y Column 3 of A234140.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2013