A223357 T(n,k)=Rolling cube face footprints: number of nXk 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

1, 4, 6, 16, 64, 36, 64, 768, 1024, 216, 256, 9216, 36864, 16384, 1296, 1024, 110592, 1327104, 1769472, 262144, 7776, 4096, 1327104, 48365568, 191102976, 84934656, 4194304, 46656, 16384, 15925248, 1764753408, 21177040896, 27518828544

Offset: 1

Author

R. H. Hardin Mar 19 2013

Keywords

• nonn
• tabl

Comments

Table starts

....1.......4.........16............64..............256................1024

....6......64........768..........9216...........110592.............1327104

...36....1024......36864.......1327104.........48365568..........1764753408

..216...16384....1769472.....191102976......21177040896.......2356125106176

.1296..262144...84934656...27518828544....9273505480704....3147420753985536

.7776.4194304.4076863488.3962711310336.4060947412942848.4204783428144463872

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A000400(n-1)

Column 2 is A013709 (n-1)

Column 3 is 16*48^(n-1)

Column 4 is 64*144^(n-1)

Row 1 is A000302(n-1)

Row 2 is 64*12^(n-2) for n>1

Formula

Empirical for column k:

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

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

k=3: a(n) = 48*a(n-1)

k=4: a(n) = 144*a(n-1)

k=5: a(n) = 480*a(n-1) -18432*a(n-2)

k=6: a(n) = 1600*a(n-1) -368640*a(n-2) [phone]*a(n-3)

k=7: a(n) = 5376*a(n-1) -5750784*a(n-2) [phone]*a(n-3) -217432719360*a(n-4)

Empirical for row n:

n=1: a(n) = 4*a(n-1)

n=2: a(n) = 12*a(n-1) for n>2

n=3: a(n) = 40*a(n-1) -128*a(n-2) for n>4

n=4: a(n) = 144*a(n-1) -3840*a(n-2) +24576*a(n-3) for n>7

n=5: [order 7] for n>11

n=6: [order 9] for n>15

n=7: [order 27] for n>33