A198717 -id:A198717 - cp's OEIS frontend

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

R. H. Hardin, Oct 29 2011

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

			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

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

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).

A214187 T(n,k)=Number of 0..6 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..6 introduced in row major order.

Original entry on oeis.org

1, 1, 4, 4, 18, 34, 11, 353, 1046, 499, 41, 7434, 147943, 108893, 10507, 162, 198052, 21418431, 96673866, 13701111, 272410, 714, 5731144, 3375824210, 76892349394, 68272896836, 1808609113, 7817980, 3397, 172707247, 537471327779

Offset: 1

R. H. Hardin Jul 07 2012

Table starts
.....1........1...........4..............11..................41
.....4.......18.........353............7434..............198052
....34.....1046......147943........21418431..........3375824210
...499...108893....96673866.....76892349394......63801460335656
.10507.13701111.68272896836.282135060192286.1213459476427300800

			Some solutions for n=4 k=1
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..3....1..2....2..3....2..0....2..0....2..3....1..2....2..0
..3..4....1..0....1..4....3..1....3..0....0..3....1..2....4..0....2..0....1..2
..2..5....3..2....5..3....4..3....2..1....3..2....0..1....3..2....1..2....2..1

R. H. Hardin, Table of n, a(n) for n = 1..71

Column 1 is A198717

cp's OEIS Frontend

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.

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