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%I A210100 #13 Jul 14 2018 07:41:27
%S A210100 7,30,135,614,2799,12766,58231,265622,1211647,5526990,25211655,
%T A210100 115004294,524598159,2392982206,10915714711,49792609142,227131616287,
%U A210100 1036072863150,4726101083175,21558359689574,98339596281519,448581262028446
%N A210100 Number of (n+1) X 2 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 A210100 Column 1 of A210107.
%H A210100 R. H. Hardin, <a href="/A210100/b210100.txt">Table of n, a(n) for n = 1..210</a>
%F A210100 Empirical: a(n) = 6*a(n-1) - 7*a(n-2) + 2*a(n-3).
%F A210100 Conjectures from _Colin Barker_, Jul 14 2018: (Start)
%F A210100 G.f.: x*(7 - 12*x + 4*x^2) / ((1 - x)*(1 - 5*x + 2*x^2)).
%F A210100 a(n) = (1/2) + (2^(-2-n)*((5-sqrt(17))^n*(-11+3*sqrt(17)) + (5+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).
%F A210100 (End)
%e A210100 Some solutions for n=4:
%e A210100 ..0..1....0..1....0..0....0..1....0..1....0..0....0..1....0..1....0..0....0..0
%e A210100 ..0..2....2..2....0..0....0..2....1..2....1..2....0..2....2..0....1..2....0..0
%e A210100 ..1..2....1..0....0..0....2..1....0..1....0..2....1..1....0..1....2..0....0..0
%e A210100 ..2..0....0..2....0..0....0..2....2..2....1..0....1..1....2..2....1..2....0..0
%e A210100 ..1..0....2..1....0..0....1..0....1..0....2..1....2..0....2..2....1..0....1..2
%Y A210100 Cf. A210107.
%K A210100 nonn
%O A210100 1,1
%A A210100 _R. H. Hardin_, Mar 17 2012

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