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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). 1
3, 8, 96, 1280, 18432, 278528, 4325376, 68157440, 1082130432, 17246978048, 275414777856, 4402341478400, 70403103916032, 1126174784749568, 18016597532737536, 288247968337756160, 4611826755915743232 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 05:34 EDT 2021. Contains 345355 sequences. (Running on oeis4.)