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

1,2

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.

Example

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

Crossrefs

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

Main diagonal is A361453.

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

Cf. A207868 (grid graph).

Sequence in context: A112709 A291573 A208353 * A200801 A241119 A208408

Adjacent sequences: A207998 A207999 A208000 * A208002 A208003 A208004

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 22 2012

Status

approved