%I #8 Jul 15 2018 12:03:22

%S 7,59,549,5167,48689,458859,4324477,40755719,384099369,3619917187,

%T 34115652149,321520538079,3030147451297,28557409213979,

%U 269137272730989,2536465091434807,23904734913837209,225288474590274099

%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..3 introduced in row major order.

%C Column 1 of A210404.

%H R. H. Hardin, <a href="/A210397/b210397.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 5*a(n-2) - 4*a(n-3).

%F Empirical g.f.: x*(1 - 2*x)*(7 + 3*x) / ((1 - x)*(1 - 9*x - 4*x^2)). - _Colin Barker_, Jul 15 2018

%e Some solutions for n=4:

%e ..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..1....0..0

%e ..0..0....0..0....0..0....1..2....0..2....2..2....0..0....0..0....0..2....0..0

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

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

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

%Y Cf. A210404.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 21 2012