A208001 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 knight-move neighbor (colorings ignoring permutations of colors).

1, 2, 2, 5, 15, 5, 15, 114, 114, 15, 52, 1657, 4141, 1657, 52, 203, 36401, 426422, 426422, 36401, 203, 877, 1094076, 86545486, 450288795, 86545486, 1094076, 877, 4140, 42436913, 29169661126, 1182700979380, 1182700979380, 29169661126, 42436913, 4140

Offset: 1

Author

R. H. Hardin, Feb 22 2012

Keywords

• nonn
• tabl

Examples

			Table starts
....1........2...........5............15............52.........203
....2.......15.........114..........1657.........36401.....1094076
....5......114........4141........426422......86545486.29169661126
...15.....1657......426422.....450288795.1182700979380
...52....36401....86545486.1182700979380
..203..1094076.29169661126
..877.42436913
.4140
...
Some solutions for n=4 k=3
..0..0..0....0..0..0....0..0..0....0..1..0....0..0..1....0..0..0....0..0..0
..1..0..1....1..2..1....1..0..1....1..0..1....0..0..1....1..0..1....1..0..1
..2..1..2....2..1..2....2..1..2....0..1..2....2..2..1....2..1..2....2..2..2
..1..0..3....3..0..0....1..0..1....1..2..1....2..3..1....1..2..1....1..0..1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..66 (terms 1..39 from R. H. Hardin).
• Eric Weisstein's World of Mathematics, Knight Graph.
• Eric Weisstein's World of Mathematics, Vertex Coloring.

Crossrefs

Columns 1..4 are A000110, A207998, A207999, A208000.

Main diagonal is A361453.

Cf. A208434 (3 colorings), A208353 (4 colorings).

Cf. A207868 (grid graph).