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

Author

R. H. Hardin Mar 21 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000400(n-1)

Column 2 is A138977

Row 1 is A000244(n-1)

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