A223269 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge

1, 4, 6, 16, 48, 36, 64, 576, 576, 216, 256, 6144, 20992, 6912, 1296, 1024, 67584, 622592, 765952, 82944, 7776, 4096, 737280, 19726336, 63438848, 27951104, 995328, 46656, 16384, 8060928, 611319808, 5889851392, 6467616768, 1020002304, 11943936

Offset

1,2

Comments

Table starts

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

....6.....48........576.........6144...........67584.............737280

...36....576......20992.......622592........19726336..........611319808

..216...6912.....765952.....63438848......5889851392.......522106961920

.1296..82944...27951104...6467616768...1771674009600....450204914417664

.7776.995328.1020002304.659411697664.534392715870208.389343801904201728

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

k=2: a(n) = 12*a(n-1)

k=3: a(n) = 40*a(n-1) -128*a(n-2)

k=4: a(n) = 112*a(n-1) -1024*a(n-2)

k=5: [order 6]

k=6: [order 9]

k=7: [order 19]

Empirical for row n:

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

n=2: a(n) = 8*a(n-1) +32*a(n-2)

n=3: a(n) = 24*a(n-1) +256*a(n-2) -1024*a(n-3) for n>4

n=4: [order 6] for n>7

n=5: [order 10] for n>11

n=6: [order 23] for n>24

Example

Some solutions for n=3 k=4
..0..3..1..2....0..1..0..1....0..4..5..1....0..4..2..4....0..2..1..3
..0..2..4..3....0..3..5..1....0..4..0..3....0..1..0..4....0..3..4..2
..4..2..1..2....0..2..0..1....3..1..5..4....3..4..0..1....0..3..4..0
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

Crossrefs

Column 1 is A000400(n-1)

Column 2 is 4*12^(n-1)

Column 3 is A223197

Row 1 is A000302(n-1)

Sequence in context: A032295 A072279 A038236 * A264471 A264477 A223357

Adjacent sequences: A223266 A223267 A223268 * A223270 A223271 A223272

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved