A198723 T(n,k) = number of n X k 0..6 arrays with values 0..6 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, 499, 2027, 499, 15, 52, 10507, 232841, 232841, 10507, 52, 203, 272410, 34003792, 173549032, 34003792, 272410, 203, 876, 7817980, 5315840795, 141168480719, 141168480719, 5315840795, 7817980, 876, 4111

Offset

1,4

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 7 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..84 from R. H. Hardin)

Example

Table starts
.....1............1...................2.......................5
.....1............4..................34.....................499
.....2...........34................2027..................232841
.....5..........499..............232841...............173549032
....15........10507............34003792............141168480719
....52.......272410..........5315840795.........116492275674072
...203......7817980........846047363854.......96356630422085931
...876....234638905.....135284283124811....79732515488691835557
..4111...7176366133...21658679381667910.65980773070548173552412
.20648.221220625936.3468618095206638077
...
Some solutions with all values 0 to 6 for n=3, k=3:
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..0....0..1..2
..3..2..4....2..3..1....3..4..5....1..3..4....3..4..3....2..3..4....3..4..3
..4..5..6....4..5..6....6..2..4....5..0..6....1..5..6....5..4..6....5..6..2

Crossrefs

Columns 1-7 are A056273(n-1), A198717, A198718, A198719, A198720, A198721, A198722.

Main diagonal is A198716.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A222340 (labeled 7 colorings), A198914 (8 colorings), A207868 (unlimited).

Sequence in context: A216663 A198906 A198982 * A198914 A207868 A135690

Adjacent sequences: A198720 A198721 A198722 * A198724 A198725 A198726

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 29 2011

Status

approved