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

1,2

Links

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

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)

Example

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

Crossrefs

Column 2 of A233202.

Sequence in context: A262465 A322491 A305678 * A368048 A245114 A276018

Adjacent sequences: A233193 A233194 A233195 * A233197 A233198 A233199

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved