A233165 Number of n X 5 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).

48, 512, 18432, 720896, 31457280, 1543503872, 83751862272, 4879082848256, 296868139499520, 18506979718725632, 1168684103302643712, 74291379453103702016, 4738507383934141071360, 302747963737721161121792

Offset

1,1

Links

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

Formula

Empirical: a(n) = 96*a(n-1) - 2048*a(n-2) for n>3.

Conjectures from Colin Barker, Oct 09 2018: (Start)

G.f.: 16*x*(3 - 256*x + 4224*x^2) / ((1 - 32*x)*(1 - 64*x)).

a(n) = 2^(5*n-6) * (2^n+28) for n>1.

(End)

Example

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

Crossrefs

Column 5 of A233168.

Sequence in context: A211149 A034778 A060674 * A247743 A189346 A334713

Adjacent sequences: A233162 A233163 A233164 * A233166 A233167 A233168

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved