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A233168 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, diagonally, 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, 1, 3, 11, 8, 8, 11, 48, 64, 96, 64, 48, 236, 512, 1280, 1280, 512, 236, 1248, 4096, 18432, 28672, 18432, 4096, 1248, 6896, 32768, 278528, 720896, 720896, 278528, 32768, 6896, 39168, 262144, 4325376, 19922944, 31457280, 19922944, 4325376 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

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

......1........1...........8.............64...............512

......3........8..........96...........1280.............18432

.....11.......64........1280..........28672............720896

.....48......512.......18432.........720896..........31457280

....236.....4096......278528.......19922944........1543503872

...1248....32768.....4325376......587202560.......83751862272

...6896...262144....68157440....17985175552.....4879082848256

..39168..2097152..1082130432...562640715776...296868139499520

.226496.16777216.17246978048.17798344474624.18506979718725632

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..544

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) = 8*a(n-1) for n>2

k=3: a(n) = 24*a(n-1) -128*a(n-2) for n>3

k=4: a(n) = 48*a(n-1) -512*a(n-2) for n>3

k=5: a(n) = 96*a(n-1) -2048*a(n-2) for n>3

k=6: a(n) = 192*a(n-1) -8192*a(n-2) for n>3

k=7: a(n) = 384*a(n-1) -32768*a(n-2) for n>3

EXAMPLE

Some solutions for n=4 k=4

..0..1..2..3....0..1..7..1....0..1..7..6....0..1..7..2....0..1..0..6

..2..4..0..1....2..3..5..3....2..3..5..4....3..2..3..1....2..3..2..4

..7..6..5..3....7..6..0..6....6..0..1..0....7..1..7..5....0..1..0..6

..2..4..0..6....3..2..3..5....4..2..3..5....4..5..4..6....3..5..3..2

CROSSREFS

Column 2 is A001018(n-2)

Sequence in context: A289066 A126970 A204134 * A001351 A216021 A327149

Adjacent sequences:  A233165 A233166 A233167 * A233169 A233170 A233171

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 05 2013

STATUS

approved

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Last modified December 2 07:02 EST 2021. Contains 349437 sequences. (Running on oeis4.)