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A223504 T(n,k)=Petersen graph (3,1) coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0 13
1, 3, 6, 9, 19, 36, 27, 115, 121, 216, 81, 631, 1519, 771, 1296, 243, 3539, 16323, 20115, 4913, 7776, 729, 19759, 182901, 426359, 266419, 31307, 46656, 2187, 110427, 2030665, 9685063, 11148439, 3528715, 199497, 279936, 6561, 617015, 22598167 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
........1........3............9..............27.................81
........6.......19..........115.............631...............3539
.......36......121.........1519...........16323.............182901
......216......771........20115..........426359............9685063
.....1296.....4913.......266419........11148439..........515473927
.....7776....31307......3528715.......291545903........27465794119
....46656...199497.....46737819......7624417031......1463848507173
...279936..1271251....619042315....199391762123.....78024299447333
..1679616..8100769...8199214219...5214442630935...4158831849750231
.10077696.51620379.108598575915.136366781617267.221674060909378867
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1)
k=2: a(n) = 7*a(n-1) -4*a(n-2)
k=3: a(n) = 15*a(n-1) -24*a(n-2) +10*a(n-3)
k=4: a(n) = 31*a(n-1) -127*a(n-2) -20*a(n-3) +705*a(n-4) -1027*a(n-5) +499*a(n-6) -60*a(n-7)
k=5: [order 21]
k=6: [order 53]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 5*a(n-1) +4*a(n-2) -4*a(n-3) for n>4
n=3: a(n) = 12*a(n-1) -4*a(n-2) -73*a(n-3) +103*a(n-4) -23*a(n-5) -16*a(n-6) +4*a(n-7) for n>8
n=4: [order 21] for n>22
n=5: [order 60] for n>61
EXAMPLE
Some solutions for n=3 k=4
..0..3..4..1....0..2..1..4....0..3..0..3....0..2..1..2....0..1..4..3
..0..3..4..3....5..2..5..4....4..1..0..1....1..2..0..2....0..1..0..3
..5..3..0..1....1..2..1..2....0..1..0..1....5..2..0..2....0..3..0..1
CROSSREFS
Column 1 is A000400(n-1)
Column 2 is A138977
Row 1 is A000244(n-1)
Sequence in context: A342596 A363124 A018186 * A322949 A285215 A015938
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 21 2013
STATUS
approved

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Last modified February 25 16:57 EST 2024. Contains 370332 sequences. (Running on oeis4.)