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A223379
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T(n,k)=3X3 square grid graph coloring a rectangular array: number of nXk 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
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9
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9, 24, 24, 68, 144, 68, 192, 912, 912, 192, 544, 5808, 13232, 5808, 544, 1536, 37008, 192752, 192752, 37008, 1536, 4352, 235824, 2812608, 6443888, 2812608, 235824, 4352, 12288, 1502736, 41044048, 215773456, 215773456, 41044048, 1502736, 12288
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OFFSET
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1,1
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COMMENTS
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Table starts
.....9........24............68..............192..................544
....24.......144...........912.............5808................37008
....68.......912.........13232...........192752..............2812608
...192......5808........192752..........6443888............215773456
...544.....37008.......2812608........215773456..........16589428016
..1536....235824......41044048.......7226963248........1275808315376
..4352...1502736.....598980512.....242067684912.......98124582178928
.12288...9575856....8741293936....8108163611488.....7547020636487088
.34816..61020048..127567402912..271587161033712...580464274863214064
.98304.388836912.1861673117136.9096958174072272.44645287470831363696
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 8*a(n-2) for n>3
k=2: a(n) = 7*a(n-1) -4*a(n-2)
k=3: a(n) = 221*a(n-2) -1718*a(n-4) +1872*a(n-6) for n>7
k=4: [order 9]
k=5: [order 28] for n>29
k=6: [order 59]
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..4..5....5..4..7..6....1..4..5..4....4..7..4..7....2..1..2..1
..1..4..5..4....2..5..8..7....4..1..4..5....3..6..3..6....5..2..5..2
..2..1..2..5....1..4..5..8....7..4..7..4....6..3..4..7....8..5..2..5
Vertex neighbors:
0 -> 1 3
1 -> 0 2 4
2 -> 1 5
3 -> 0 4 6
4 -> 3 1 5 7
5 -> 4 2 8
6 -> 3 7
7 -> 6 4 8
8 -> 7 5
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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