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A198906 T(n,k) = number of n X k 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor. 17
1, 1, 1, 2, 4, 2, 5, 33, 33, 5, 15, 380, 1211, 380, 15, 51, 4801, 50384, 50384, 4801, 51, 187, 62004, 2125425, 6907736, 2125425, 62004, 187, 715, 804833, 89793204, 948656912, 948656912, 89793204, 804833, 715, 2795, 10459180, 3794115705 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Number of colorings of the grid graph P_n X P_k using a maximum of 5 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..378 (terms 1..127 from R. H. Hardin)
EXAMPLE
Table starts
.....1..........1...............2....................5
.....1..........4..............33..................380
.....2.........33............1211................50384
.....5........380...........50384..............6907736
....15.......4801.........2125425............948656912
....51......62004........89793204.........130292546801
...187.....804833......3794115705.......17895005957823
...715...10459180....160319061892.....2457786852894234
..2795..135958401...6774239755817...337564362706067534
.11051.1767426404.286243775060868.46362726246946052884
...
Some solutions with values 0 to 4 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..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0
..0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
..2..0..2..0....2..0..3..0....2..0..2..3....2..0..1..0....2..0..1..3
..3..2..1..4....0..1..0..4....0..4..0..2....3..2..4..3....0..3..4..2
..2..4..2..1....2..4..3..1....1..3..1..4....1..0..1..2....4..0..1..4
CROSSREFS
Columns 1-7 are A007581(n-2), A198900, A198901, A198902, A198903, A198904, A198905.
Main diagonal is A198899.
Cf. A207997 (3 colorings), A198715 (4 colorings), A222144 (labeled 5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).
Sequence in context: A085843 A198715 A216663 * A198982 A198723 A198914
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 31 2011
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)