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

Author

R. H. Hardin, Feb 22 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

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

Crossrefs

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

Main diagonal is A289136.

Cf. A207868, A212208, A212209.