A233167 Number of n X 7 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 (unlabeled 8-colorings with no clashing color pairs).

1248, 32768, 4325376, 587202560, 83751862272, 12919261626368, 2216615441596416, 427841964600197120, 91657259616244334592, 21176862196618565255168, 5128490000396434702073856

Offset

1,1

Links

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

Formula

Empirical: a(n) = 384*a(n-1) - 32768*a(n-2) for n>3.

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

G.f.: 32*x*(39 - 13952*x + 1019904*x^2) / ((1 - 128*x)*(1 - 256*x)).

a(n) = 2^(7*n-6) * (2^n+124) for n>1. (End)

Example

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

Crossrefs

Column 7 of A233168.

Sequence in context: A234212 A047629 A221012 * A266037 A233179 A224435

Adjacent sequences: A233164 A233165 A233166 * A233168 A233169 A233170

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved