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Number of (n+1) X 3 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
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%I #16 Jun 13 2018 14:48:34

%S 564,6668,91924,1269044,17521788,241927532,3340355572,46121153588,

%T 636806710044,8792555155244,121401086008468,1676216233423412,

%U 23143951620064572,319554533544992108,4412172198832106164

%N Number of (n+1) X 3 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.

%C Column 2 of A206137.

%H R. H. Hardin, <a href="/A206131/b206131.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) - 47*a(n-2) + 41*a(n-3) - 10*a(n-4) for n > 5.

%F Empirical g.f.: 4*x*(3 - 5*x)*(47 - 165*x + 148*x^2 - 36*x^3) / ((1 - x)*(1 - 16*x + 31*x^2 - 10*x^3)). - _Colin Barker_, Jun 13 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A206137.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012