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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. 16
 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 Adjacent sequences:  A198903 A198904 A198905 * A198907 A198908 A198909 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Oct 31 2011 STATUS approved

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Last modified August 9 09:43 EDT 2022. Contains 356021 sequences. (Running on oeis4.)