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A233129 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs) 8
1, 1, 1, 3, 8, 3, 10, 80, 80, 10, 36, 896, 2688, 896, 36, 136, 10496, 96256, 96256, 10496, 136, 528, 124928, 3497984, 10674176, 3497984, 124928, 528, 2080, 1495040, 127533056, 1189609472, 1189609472, 127533056, 1495040, 2080, 8256, 17924096 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

.....1..........1...............3...................10

.....1..........8..............80..................896

.....3.........80............2688................96256

....10........896...........96256.............10674176

....36......10496.........3497984...........1189609472

...136.....124928.......127533056.........132682612736

...528....1495040......4653056000.......14800557965312

..2080...17924096....169793814528.....1651015493353472

..8256..215023616...6196127858688...184172904936636416

.32896.2580021248.226111237652480.20544737466392772608

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

FORMULA

Empirical for column k:

k=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3

k=2: a(n) = 16*a(n-1) -48*a(n-2)

k=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)

k=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)

k=5: [order 6]

k=6: [order 8]

k=7: [order 14]

Empirical for row n:

n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3

n=2: a(n) = 16*a(n-1) -48*a(n-2)

n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)

n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)

n=5: [order 6]

n=6: [order 8]

n=7: [order 14]

EXAMPLE

Some solutions for n=3 k=4

..0..1..0..1....0..1..5..2....0..1..2..4....0..1..5..4....0..1..0..4

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

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

CROSSREFS

Column 1 is A007582(n-2)

Sequence in context: A016623 A273100 A046543 * A035292 A144457 A220138

Adjacent sequences:  A233126 A233127 A233128 * A233130 A233131 A233132

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 04 2013

STATUS

approved

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Last modified April 25 18:12 EDT 2019. Contains 322461 sequences. (Running on oeis4.)