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%I #13 Jul 14 2018 15:34:32
%S 30,225,1690,12725,95830,721705,5435250,40933565,308275950,2321665905,
%T 17484765130,131680019525,991699197190,7468614458425,56247097997730,
%U 423604143817805,3190217398715550,24025938366280065,180942438158822650
%N Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.
%C Column 2 of A210107.
%H R. H. Hardin, <a href="/A210101/b210101.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 3*a(n-2) - 4*a(n-3).
%F Conjectures from _Colin Barker_, Jul 14 2018: (Start)
%F G.f.: 5*x*(6 - 3*x - 4*x^2) / ((1 - x)*(1 - 7*x - 4*x^2)).
%F a(n) = (1/13)*2^(-2-n)*(13*2^(1+n) + (117-11*sqrt(65))*(7-sqrt(65))^n + (7+sqrt(65))^n*(117+11*sqrt(65))).
%F (End)
%e Some solutions for n=4:
%e 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 2 0 1 2
%e 0 0 0 0 0 0 1 2 0 2 1 2 0 0 2 0 2 0 1 2 0
%e 1 2 1 0 0 0 1 0 1 2 0 1 2 1 1 2 1 2 1 0 1
%e 1 0 2 0 0 0 0 2 0 0 1 2 2 0 2 1 0 1 0 2 2
%e 0 2 1 0 0 0 2 1 2 0 2 0 2 1 0 0 2 2 2 1 0
%Y Cf. A210107.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 17 2012
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