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 A208001 T(n,k)=Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors). 6
 1, 2, 2, 5, 15, 5, 15, 114, 114, 15, 52, 1657, 4141, 1657, 52, 203, 36401, 426422, 426422, 36401, 203, 877, 1094076, 86545486, 450288795, 86545486, 1094076, 877, 4140, 42436913, 29169661126, 1182700979380, 1182700979380, 29169661126, 42436913, 4140 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..66 (terms 1..39 from R. H. Hardin). Eric Weisstein's World of Mathematics, Knight Graph. Eric Weisstein's World of Mathematics, Vertex Coloring. EXAMPLE Table starts ....1........2...........5............15............52.........203 ....2.......15.........114..........1657.........36401.....1094076 ....5......114........4141........426422......86545486.29169661126 ...15.....1657......426422.....450288795.1182700979380 ...52....36401....86545486.1182700979380 ..203..1094076.29169661126 ..877.42436913 .4140 ... Some solutions for n=4 k=3 ..0..0..0....0..0..0....0..0..0....0..1..0....0..0..1....0..0..0....0..0..0 ..1..0..1....1..2..1....1..0..1....1..0..1....0..0..1....1..0..1....1..0..1 ..2..1..2....2..1..2....2..1..2....0..1..2....2..2..1....2..1..2....2..2..2 ..1..0..3....3..0..0....1..0..1....1..2..1....2..3..1....1..2..1....1..0..1 CROSSREFS Columns 1..4 are A000110, A207998, A207999, A208000. Main diagonal is A361453. Cf. A208434 (3 colorings), A208353 (4 colorings). Cf. A207868 (grid graph). Sequence in context: A112709 A291573 A208353 * A200801 A241119 A208408 Adjacent sequences: A207998 A207999 A208000 * A208002 A208003 A208004 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 22 2012 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)