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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) 8
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 (list; table; graph; refs; listen; history; text; internal format)
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: A252748 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

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)