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A233196 Number of n X 2 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). 1
1, 3, 36, 528, 8256, 131328, 2098176, 33558528, 536887296, 8590000128, 137439215616, 2199024304128, 35184376283136, 562949970198528, 9007199321849856, 144115188344291328, 2305843010287435776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

Empirical: a(n) = 20*a(n-1) - 64*a(n-2) for n>3.

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: x*(1 - 17*x + 40*x^2) / ((1 - 4*x)*(1 - 16*x)).

a(n) = 2^(2*n-7) * (4^n+8) for n>1.

(End)

EXAMPLE

Some solutions for n=5:

..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1

..2..3....2..3....2..0....2..3....2..0....2..7....2..0....2..7....2..3....2..0

..7..1....0..2....3..6....1..0....3..6....6..3....3..1....6..2....7..6....3..6

..4..0....3..7....2..4....3..1....0..2....5..7....2..4....3..1....3..5....7..5

..6..4....1..4....1..0....5..3....3..7....3..1....0..2....0..5....7..4....3..0

CROSSREFS

Column 2 of A233202.

Sequence in context: A262465 A322491 A305678 * A245114 A276018 A291096

Adjacent sequences:  A233193 A233194 A233195 * A233197 A233198 A233199

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 05 2013

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)