A233196 Number of n X 2 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, 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 (unlabeled 8-colorings with no clashing color pairs).

1, 3, 36, 528, 8256, 131328, 2098176, 33558528, 536887296, 8590000128, 137439215616, 2199024304128, 35184376283136, 562949970198528, 9007199321849856, 144115188344291328, 2305843010287435776

Offset: 1

Author

R. H. Hardin, Dec 05 2013

Keywords

• nonn

Examples

			Some solutions for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..0....2..3....2..0....2..7....2..0....2..7....2..3....2..0
..7..1....0..2....3..6....1..0....3..6....6..3....3..1....6..2....7..6....3..6
..4..0....3..7....2..4....3..1....0..2....5..7....2..4....3..1....3..5....7..5
..6..4....1..4....1..0....5..3....3..7....3..1....0..2....0..5....7..4....3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 2 of A233202.

Formula

Empirical: a(n) = 20*a(n-1) - 64*a(n-2) for n>3.

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: x*(1 - 17*x + 40*x^2) / ((1 - 4*x)*(1 - 16*x)).

a(n) = 2^(2*n-7) * (4^n+8) for n>1.

(End)