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A208021 T(n,k) = Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors). 6
1, 1, 1, 2, 1, 2, 5, 7, 7, 5, 15, 87, 270, 87, 15, 52, 1657, 27093, 27093, 1657, 52, 203, 43833, 5252041, 30066912, 5252041, 43833, 203, 877, 1515903, 1688298227, 80318704605, 80318704605, 1688298227, 1515903, 877, 4140, 65766991 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Equivalently, the number of colorings of the n x k king graph using any number of colors up to permutation of the colors. - Andrew Howroyd, Jun 25 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..231 (terms 1..49 from R. H. Hardin)

Eric Weisstein's World of Mathematics, King Graph

EXAMPLE

Table starts

...1........1............2...............5...............15..............52

...1........1............7..............87.............1657...........43833

...2........7..........270...........27093..........5252041......1688298227

...5.......87........27093........30066912......80318704605.421673189900658

..15.....1657......5252041.....80318704605.3662498214110836

..52....43833...1688298227.421673189900658

.203..1515903.819147302097

.877.65766991

...

Some solutions for n=4 k=3

..0..1..2....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..2

..2..3..4....2..3..2....2..3..2....2..3..2....2..3..2....2..3..2....2..3..0

..5..6..0....4..0..4....0..1..0....4..1..0....0..1..0....0..4..0....4..5..4

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

CROSSREFS

Columns 1-5 are A000110(n-1), A020556(n-1), A208018, A208019, A208020.

Main diagonal is A289136.

Cf. A207868, A212208, A212209.

Sequence in context: A296666 A120898 A153910 * A052532 A006702 A129394

Adjacent sequences:  A208018 A208019 A208020 * A208022 A208023 A208024

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 22 2012

STATUS

approved

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Last modified July 3 18:10 EDT 2022. Contains 355055 sequences. (Running on oeis4.)