A233202 T(n,k)=Number of nXk 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, 1, 3, 3, 3, 11, 36, 36, 11, 48, 528, 1440, 528, 48, 236, 8256, 62720, 62720, 8256, 236, 1248, 131328, 2779136, 7802880, 2779136, 131328, 1248, 6896, 2098176, 123551744, 981532672, 981532672, 123551744, 2098176, 6896, 39168, 33558528

Offset

1,4

Comments

Table starts

....1.......1..........3.............11................48...................236

....1.......3.........36............528..............8256................131328

....3......36.......1440..........62720...........2779136.............123551744

...11.....528......62720........7802880.........981532672..........123833679872

...48....8256....2779136......981532672......352524959744.......127365174788096

..236..131328..123551744...123833679872...127365174788096....132364161848967168

.1248.2098176.5496242176.15635845218304.46111939268444160.138127371171167993856

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4

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

k=3: a(n) = 64*a(n-1) -960*a(n-2) +4096*a(n-3) for n>4

k=4: [order 5] for n>6

k=5: [order 10] for n>11

k=6: [order 22] for n>23

Example

Some solutions for n=3 k=4
..0..1..2..7....0..1..2..0....0..1..2..3....0..1..2..7....0..1..7..2
..3..7..4..5....5..3..6..3....5..4..6..5....5..7..3..6....5..3..6..4
..6..5..7..6....6..7..2..6....6..2..3..6....3..5..0..3....6..7..2..6

Crossrefs

Column 1 is A233162

Sequence in context: A346869 A097161 A274993 * A101480 A156715 A133797

Adjacent sequences: A233199 A233200 A233201 * A233203 A233204 A233205

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 05 2013

Status

approved