The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198715 T(n,k)=Number of nXk 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor. 16
 1, 1, 1, 2, 4, 2, 5, 25, 25, 5, 14, 172, 401, 172, 14, 41, 1201, 6548, 6548, 1201, 41, 122, 8404, 107042, 250031, 107042, 8404, 122, 365, 58825, 1749965, 9548295, 9548295, 1749965, 58825, 365, 1094, 411772, 28609241, 364637102, 851787199, 364637102 (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 4 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..496 (terms 1..180 from R. H. Hardin) Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Vertex Coloring Wikipedia, Graph Coloring EXAMPLE Table starts ....1........1............2...............5..................14 ....1........4...........25.............172................1201 ....2.......25..........401............6548..............107042 ....5......172.........6548..........250031.............9548295 ...14.....1201.......107042.........9548295...........851787199 ...41.....8404......1749965.......364637102.........75987485516 ..122....58825.....28609241.....13925032958.......6778819400772 ..365...411772....467717288....531779578441.....604736581320925 .1094..2882401...7646461682..20307996787865...53948385378521909 .3281.20176804.125007943505.775536991678112.4812720805166620356 ... Some solutions with all values from 0 to 3 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..2..1....0..1..0..1....0..1..0..1....0..1..0..2....0..1..0..1 ..1..2..0..3....2..0..3..0....2..0..1..0....1..2..1..3....1..2..3..0 ..2..0..2..0....1..3..0..2....3..2..0..2....0..3..0..2....3..1..2..3 ..3..2..0..1....3..2..1..0....0..3..2..1....3..1..3..0....1..3..1..0 CROSSREFS Columns 1-7 are A007051(n-2), A034494(n-1), A198710, A198711, A198712, A198713, A198714. Main diagonal is A198709. Cf. A207997 (3 colorings), A222444 (labeled 4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited). Sequence in context: A085880 A055883 A085843 * A216663 A198906 A198982 Adjacent sequences:  A198712 A198713 A198714 * A198716 A198717 A198718 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Oct 29 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 17 21:56 EDT 2022. Contains 356189 sequences. (Running on oeis4.)