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

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

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

R. H. Hardin, Table of n, a(n) for n = 1..199

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

Adjacent sequences: A223501 A223502 A223503 * A223505 A223506 A223507

Keyword

nonn,tabl

Author

R. H. Hardin Mar 21 2013

Status

approved