Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/VertexColoring.html">Vertex Coloring</a>
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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R. H. Hardin, Andrew Howroyd, <a href="/A198715/b198715_1.txt">Table of n, a(n) for n = 1..496</a> (terms 1..180</a> from R. H. Hardin)
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>
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
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.
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
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
...
Column Columns 1 is -7 are 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).
R. H. Hardin , Oct 29 2011
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