A233197 Number of n X 3 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 (unlabelled 8-colorings with no clashing color pairs).

3, 36, 1440, 62720, 2779136, 123551744, 5496242176, 244533166080, 10879798083584, 484067845865472, 21537343823413248, 958248525617954816, 42634797465737363456, 1896925413514655301632, 84398806858761213313024

Offset

1,1

Links

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

Formula

Empirical: a(n) = 64*a(n-1) - 960*a(n-2) + 4096*a(n-3) for n>4.

Empirical g.f.: x*(3 - 156*x + 2016*x^2 - 7168*x^3) / ((1 - 8*x)*(1 - 56*x + 512*x^2)). - Colin Barker, Oct 10 2018

Example

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

Crossrefs

Column 3 of A233202.

Sequence in context: A126447 A102921 A265475 * A300770 A272660 A193302

Adjacent sequences: A233194 A233195 A233196 * A233198 A233199 A233200

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved