%I #8 Oct 09 2018 14:55:44
%S 3,8,96,1280,18432,278528,4325376,68157440,1082130432,17246978048,
%T 275414777856,4402341478400,70403103916032,1126174784749568,
%U 18016597532737536,288247968337756160,4611826755915743232
%N Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
%H R. H. Hardin, <a href="/A233163/b233163.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 24*a(n-1) - 128*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Oct 09 2018: (Start)
%F G.f.: x*(3 - 64*x + 288*x^2) / ((1 - 8*x)*(1 - 16*x)).
%F a(n) = 8^(n-2) * (2^n+4) for n>1.
%F (End)
%e Some solutions for n=5:
%e ..0..1..2....0..1..7....0..1..0....0..1..7....0..1..0....0..1..2....0..1..7
%e ..5..3..7....2..3..2....2..3..5....2..3..2....2..3..2....5..3..7....2..3..2
%e ..0..6..2....6..0..1....1..0..1....0..6..7....0..1..7....7..1..5....0..1..0
%e ..5..4..0....3..2..3....3..5..4....4..5..3....3..5..4....2..4..7....4..2..3
%e ..7..6..5....1..0..1....0..1..7....1..7..6....7..6..7....0..6..5....6..0..6
%Y Column 3 of A233168.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2013