%I #8 Jun 13 2018 14:08:56

%S 85,1070,17142,238182,3814022,53494742,850283062,12012206406,

%T 189640648294,2696243766070,42310772017430,604975719064998,

%U 9442901799738950,135699248890772630,2108048210361864694

%N Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.

%C Column 2 of A206169.

%H R. H. Hardin, <a href="/A206163/b206163.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 217*a(n-2) - 33*a(n-3) - 1320*a(n-4) - 432*a(n-5) + 1152*a(n-6) for n>7.

%F Empirical g.f.: x*(85 + 985*x - 2373*x^2 - 8345*x^3 + 3536*x^4 + 10032*x^5 - 2688*x^6) / ((1 - x - 4*x^2)*(1 - 213*x^2 - 180*x^3 + 288*x^4)). - _Colin Barker_, Jun 13 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A206169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012