A233163 Number of n X 3 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).

3, 8, 96, 1280, 18432, 278528, 4325376, 68157440, 1082130432, 17246978048, 275414777856, 4402341478400, 70403103916032, 1126174784749568, 18016597532737536, 288247968337756160, 4611826755915743232

Offset

1,1

Links

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

Formula

Empirical: a(n) = 24*a(n-1) - 128*a(n-2) for n>3.

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

G.f.: x*(3 - 64*x + 288*x^2) / ((1 - 8*x)*(1 - 16*x)).

a(n) = 8^(n-2) * (2^n+4) for n>1.

(End)

Example

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

Crossrefs

Column 3 of A233168.

Sequence in context: A266671 A069703 A114737 * A281709 A099296 A066619

Adjacent sequences: A233160 A233161 A233162 * A233164 A233165 A233166

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved