A198914 T(n,k) = number of n X k 0..7 arrays with values 0..7 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, 500, 2051, 500, 15, 52, 10867, 269940, 269940, 10867, 52, 203, 313132, 54381563, 319608038, 54381563, 313132, 203, 877, 10856948, 13088156547, 481871809749, 481871809749, 13088156547, 10856948, 877, 4139

Offset

1,4

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 8 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..276 (terms 1..71 from R. H. Hardin)

Example

Table starts
.....1............1..................2......................5
.....1............4.................34....................500
.....2...........34...............2051.................269940
.....5..........500.............269940..............319608038
....15........10867...........54381563...........481871809749
....52.......313132........13088156547........769126451071174
...203.....10856948......3352514013159....1243368053336112649
...877....418689772....876632051686733.2015791720035206825303
..4139..17067989413.230783525290600476
.21110.715189507700
...
Some solutions with values 0 to 7 for n=5, k=3:
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..1..2..1....1..0..1....1..2..1....1..0..2....1..0..2....1..2..3....1..2..3
..3..0..2....2..3..4....3..4..2....3..4..5....3..4..5....0..1..4....0..4..5
..2..4..5....5..4..3....5..6..1....5..3..6....6..7..0....5..6..7....1..5..1
..1..6..7....6..0..7....6..7..2....7..4..2....3..0..3....7..0..5....6..7..4

Crossrefs

Columns 1-7 are A099262(n-1), A198908, A198909, A198910, A198911, A198912, A198913.

Main diagonal is A198907.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A222462 (labeled 8 colorings), A207868 (unlimited).

Sequence in context: A198906 A198982 A198723 * A207868 A135690 A010241

Adjacent sequences: A198911 A198912 A198913 * A198915 A198916 A198917

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 31 2011

Status

approved