A233166 Number of n X 6 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).

236, 4096, 278528, 19922944, 1543503872, 133143986176, 12919261626368, 1389782697508864, 161003686678495232, 19527607984278470656, 2430358531711233425408, 306658673481347586064384

Offset

1,1

Links

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

Formula

Empirical: a(n) = 192*a(n-1) - 8192*a(n-2) for n>3.

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

G.f.: 4*x*(59 - 10304*x + 356352*x^2) / ((1 - 64*x)*(1 - 128*x)).

a(n) = 64^(n-1) * (2^n+60) for n>1.

(End)

Example

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

Crossrefs

Column 6 of A233168.

Sequence in context: A251491 A251484 A247475 * A138820 A218649 A285156

Adjacent sequences: A233163 A233164 A233165 * A233167 A233168 A233169

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved