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| A198715
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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.
(history;
published version)
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#14 by OEIS Server at Tue Jun 27 21:39:47 EDT 2017
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| LINKS
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Andrew Howroyd, <a href="/A198715/b198715_1.txt">Table of n, a(n) for n = 1..496</a> (terms 1..180 from R. H. Hardin)
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#13 by N. J. A. Sloane at Tue Jun 27 21:39:47 EDT 2017
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Discussion
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| Tue Jun 27
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| OEIS Server: Installed new b-file as b198715.txt. Old b-file is now b198715_1.txt.
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#12 by Michel Marcus at Tue Jun 27 11:22:48 EDT 2017
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#11 by Michel Marcus at Tue Jun 27 11:22:42 EDT 2017
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#10 by Andrew Howroyd at Tue Jun 27 11:08:08 EDT 2017
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#9 by Andrew Howroyd at Mon Jun 26 23:53:43 EDT 2017
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| LINKS
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R. H. HardinAndrew Howroyd, <a href="/A198715/b198715_1.txt">Table of n, a(n) for n = 1..180496</a>> (terms 1..180 from R. H. Hardin)
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#8 by Andrew Howroyd at Mon Jun 26 20:09:46 EDT 2017
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/VertexColoring.html">Vertex Coloring</a>
Wikipedia, <a href="https://en.wikipedia.org/wiki/Graph_coloring">Graph Coloring</a>
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#7 by Andrew Howroyd at Mon Jun 26 19:55:48 EDT 2017
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| COMMENTS
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Number of 4-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
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#6 by Andrew Howroyd at Mon Jun 26 19:27:14 EDT 2017
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| NAME
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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.
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| COMMENTS
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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
Number of 4-colorings of the grid graph P_n X P_k up to permutation of the colors. - Andrew Howroyd, Jun 26 2017
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| EXAMPLE
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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
...
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| CROSSREFS
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ColumnColumns 1-7 isare A007051(n-2)), A034494(n-1), A198710, A198711, A198712-A198714.
Column 2 is A034494(n-1)
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).
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| AUTHOR
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_R. H. Hardin_ _, Oct 29 2011
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| STATUS
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approved
editing
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#5 by Russ Cox at Sat Mar 31 12:36:35 EDT 2012
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| AUTHOR
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_R. H. Hardin (rhhardin(AT)att.net) _ Oct 29 2011
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Discussion
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| Sat Mar 31
| 12:36
| OEIS Server: https://oeis.org/edit/global/875
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