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

Author

R. H. Hardin Mar 22 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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)

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