A223556 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 or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

1, 3, 6, 9, 27, 36, 27, 171, 243, 216, 81, 1089, 3249, 2187, 1296, 243, 6939, 44217, 61731, 19683, 7776, 729, 44217, 609309, 1795473, 1172889, 177147, 46656, 2187, 281763, 8410671, 53599905, 72906921, 22284891, 1594323, 279936, 6561, 1795473

Offset

1,2

Comments

Table starts

........1..........3.............9...............27...................81

........6.........27...........171.............1089.................6939

.......36........243..........3249............44217...............609309

......216.......2187.........61731..........1795473.............53599905

.....1296......19683.......1172889.........72906921...........4715559621

.....7776.....177147......22284891.......2960456193.........414863325945

....46656....1594323.....423412929.....120212193177.......36498667573629

...279936...14348907....8044845651....4881332621169.....3211064180380305

..1679616..129140163..152852067369..198211242377097...282501632829717621

.10077696.1162261467.2904189280011.8048559615522273.24853807982558115945

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1)

k=2: a(n) = 9*a(n-1)

k=3: a(n) = 19*a(n-1)

k=4: a(n) = 41*a(n-1) -16*a(n-2)

k=5: a(n) = 95*a(n-1) -626*a(n-2) +720*a(n-3) for n>4

k=6: [order 8] for n>9

k=7: [order 13] for n>15

Empirical for row n:

n=1: a(n) = 3*a(n-1)

n=2: a(n) = 7*a(n-1) -4*a(n-2) for n>3

n=3: a(n) = 17*a(n-1) -47*a(n-2) +41*a(n-3) -10*a(n-4) for n>6

n=4: [order 13] for n>16

n=5: [order 41] for n>45

Example

Some solutions for n=3 k=4
..0..3..5..2....0..1..4..1....0..2..5..2....0..2..5..2....0..1..2..0
..5..3..0..1....0..1..0..3....1..2..5..2....5..2..1..4....2..0..1..2
..4..3..4..3....2..1..4..5....0..2..0..1....1..2..1..2....1..4..5..3

Crossrefs

Column 1 is A000400(n-1)

Column 2 is A013708(n-1)

Column 3 = 9*19^(n-1) is row 8 of A223556 with T(2+,3) = A121057(8,1+)

Row 1 is A000244(n-1)

Sequence in context: A301536 A296110 A019461 * A067862 A062927 A349597

Adjacent sequences: A223553 A223554 A223555 * A223557 A223558 A223559

Keyword

nonn,tabl

Author

R. H. Hardin Mar 22 2013

Status

approved