A198982 T(n,k) = number of n X k 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 481, 1835, 481, 15, 52, 8731, 146286, 146286, 8731, 52, 202, 174454, 12662226, 53082012, 12662226, 174454, 202, 855, 3603244, 1112962873, 19622872903, 19622872903, 1112962873, 3603244, 855, 3845, 75251971

Offset: 1

Author

R. H. Hardin, Nov 01 2011

Keywords

• nonn
• tabl

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 6 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
.....1...........1.................2........................5
.....1...........4................34......................481
.....2..........34..............1835...................146286
.....5.........481............146286.................53082012
....15........8731..........12662226..............19622872903
....52......174454........1112962873............7267830860056
...202.....3603244.......98102456246.........2692353648978984
...855....75251971.....8651794282083.......997397244990907738
..3845..1577395861...763087851014929....369492074075459555844
.18002.33105096904.67305520316532514.136880688981914387733120
...
Some solutions with all values from 0 to 5 for n=6, k=4:
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0
..0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1
..2..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0
..1..2..0..2....4..1..0..1....3..1..0..4....3..4..2..1....3..4..2..5
..4..5..2..1....5..4..2..4....5..2..3..1....1..5..1..5....5..1..5..2
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..111 from R. H. Hardin)

Crossrefs

Columns 1-7 are A056272(n-1), A198976, A198977, A198978, A198979, A198980, A198981.

Main diagonal is A198975.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A222281 (labeled 6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).