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).

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

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