%I #11 Jul 14 2018 15:34:45

%S 44,481,5587,67585,836053,10466659,131849767,1666227265,21090849853,

%T 267184911211,3386189676751,42924236694073,544177325000245,

%U 6899249896382995,87473246343061879,1109059012082436337

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

%C Column 2 of A210125.

%H R. H. Hardin, <a href="/A210119/b210119.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) - 174*a(n-2) + 368*a(n-3) + 303*a(n-4) - 888*a(n-5) - 340*a(n-6) + 240*a(n-7).

%F Empirical g.f.: x*(44 - 575*x + 1699*x^2 + 999*x^3 - 4189*x^4 - 1510*x^5 + 1120*x^6) / ((1 - 6*x - 3*x^2 + 2*x^3)*(1 - 18*x + 69*x^2 - 10*x^3 - 120*x^4)). - _Colin Barker_, Jul 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A210125.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 17 2012