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 A207997 T(n,k) = number of n X k 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors). 19
 1, 1, 1, 2, 3, 2, 4, 9, 9, 4, 8, 27, 41, 27, 8, 16, 81, 187, 187, 81, 16, 32, 243, 853, 1302, 853, 243, 32, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 128, 2187, 17749, 63267, 96831, 63267, 17749, 2187, 128, 256, 6561, 80963, 441090, 1034073, 1034073, 441090, 80963 (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 3 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017 LINKS R. H. Hardin, Table of n, a(n) for n = 1..544 R. J. Mathar, Counting 2-way monotonic terrace forms over rectangular landscapes, vixra:1511.0225, eq. (33)-(35). Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Vertex Coloring Wikipedia, Graph Coloring FORMULA 2*T(n,m) = A078099(n,m) for m>1. - R. J. Mathar, Nov 23 2015 EXAMPLE Table starts ..1....1.....2.......4.........8.........16...........32............64 ..1....3.....9......27........81........243..........729..........2187 ..2....9....41.....187.......853.......3891........17749.........80963 ..4...27...187....1302......9075......63267.......441090.......3075255 ..8...81...853....9075.....96831....1034073.....11045757.....117997043 .16..243..3891...63267...1034073...16932816....277458045....4547477370 .32..729.17749..441090..11045757..277458045...6978332618..175605187731 .64.2187.80963.3075255.117997043.4547477370.175605187731.6787438272198 ... Some solutions for n=4, k=3: ..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0 ..2..0..1....2..0..2....1..0..2....1..2..1....2..0..1....1..2..1....1..2..1 ..0..2..0....0..1..0....2..1..0....0..1..2....0..2..0....0..1..2....2..0..2 ..1..0..1....1..2..1....1..0..1....1..2..0....2..0..2....2..0..1....1..2..0 CROSSREFS Cf. A020698 (column 3), A078100 (column 4), A207994 (column 5), A207995 (column 6), A207996 (column 7). Main diagonal is A207993. Cf. A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited). Sequence in context: A247936 A231150 A274858 * A304489 A034800 A082771 Adjacent sequences: A207994 A207995 A207996 * A207998 A207999 A208000 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 22 2012 STATUS approved

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Last modified July 21 03:43 EDT 2024. Contains 374463 sequences. (Running on oeis4.)