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A223599 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 13
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Column 1 is A001025
Column 2 is A223434
Row 1 is A188825(n+1)
Sequence in context: A109098 A223395 A202329 * A223692 A165115 A165117
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 23 2013
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)