A233129 T(n,k) = number of n X k 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 (unlabeled 6-colorings with no clashing color pairs).

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

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 A387661 A144457

Adjacent sequences: A233126 A233127 A233128 * A233130 A233131 A233132

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 04 2013

Status

approved