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%I #9 Jul 14 2018 05:56:01
%S 9,51,323,2187,15435,111659,819243,6058155,44991659,334914219,
%T 2496201387,18617371307,138903833259,1036559854251,7736058194603,
%U 57739004914347,430954921634475,3216631813810859,24009028665518763,179204877435185835
%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one, two or four distinct values, and new values 0..3 introduced in row major order.
%C Column 1 of A210061.
%H R. H. Hardin, <a href="/A210054/b210054.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) - 48*a(n-2) + 52*a(n-3) - 16*a(n-4).
%F Conjectures from _Colin Barker_, Jul 14 2018: (Start)
%F G.f.: x*(9 - 66*x + 92*x^2 - 32*x^3) / ((1 - x)*(1 - 4*x)*(1 - 8*x + 4*x^2)).
%F a(n) = (1/3) + 4^n - (1/6)*(4-2*sqrt(3))^n*(-2+sqrt(3)) + (1/3)*2^(-1+n)*(2+sqrt(3))^(1+n).
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..1....0..0....0..1....0..0....0..1....0..0....0..0....0..1....0..1
%e ..0..0....0..1....0..0....1..0....0..0....1..0....1..0....0..0....1..0....2..3
%e ..0..1....0..0....0..0....0..0....1..0....0..0....0..1....1..1....2..3....1..0
%e ..1..1....0..1....1..0....2..0....1..0....0..1....1..0....2..1....1..0....0..0
%e ..0..0....1..1....2..3....0..2....0..0....0..0....0..0....2..2....0..0....0..0
%Y Cf. A210061.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 16 2012
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