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

Author

R. H. Hardin, Dec 05 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A233162

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