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

Author

R. H. Hardin, Dec 04 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A007582(n-2).

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]