%I #9 May 25 2021 05:18:42

%S 0,6,48,438,3936,35430,318864,2869782,25828032,232452294,2092070640,

%T 18828635766,169457721888,1525119496998,13726075472976,

%U 123534679256790,1111812113311104,10006309019799942,90056781178199472,810511030603795254

%N Number of n X 4 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

%H R. H. Hardin, <a href="/A231104/b231104.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) + 9*a(n-2).

%F Conjectures from _Colin Barker_, Sep 26 2018: (Start)

%F G.f.: 6*x^2 / ((1 + x)*(1 - 9*x)).

%F a(n) = (9^n + 9) / 15 for n even.

%F a(n) = (9^n - 9) / 15 for n odd.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 4 of A231108.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 03 2013