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A223599
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T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph
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13
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16, 48, 256, 144, 256, 4096, 432, 1504, 1376, 65536, 1296, 6736, 16192, 7424, 1048576, 3888, 32768, 122608, 176224, 40160, 16777216, 11664, 156592, 1124064, 2372080, 1931968, 217600, 268435456, 34992, 755200, 9902320, 43725920, 47659632
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OFFSET
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1,1
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COMMENTS
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Table starts
............16........48..........144.............432...............1296
...........256.......256.........1504............6736..............32768
..........4096......1376........16192..........122608............1124064
.........65536......7424.......176224.........2372080...........43725920
.......1048576.....40160......1931968........47659632.........1807461152
......16777216....217600.....21308000.......982848688........77164934624
.....268435456...1180256....236213312.....20631729648......3355919411936
....4294967296...6405888...2629972704....438231627440....147579242411936
...68719476736..34782688..29389265856...9379905920496...6534353238114336
.1099511627776.188912640.329426847840.201754894742320.290550417324168160
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 16*a(n-1)
k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
k=3: a(n) = 23*a(n-1) -153*a(n-2) +217*a(n-3) +258*a(n-4) -456*a(n-5) -104*a(n-6) +192*a(n-7)
k=4: [order 9]
k=5: [order 29]
k=6: [order 55]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6
n=3: [order 11] for n>12
n=4: [order 28] for n>29
n=5: [order 74] for n>75
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EXAMPLE
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Some solutions for n=3 k=4
.14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10
..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14
..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14
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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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