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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 12
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 19 2013
STATUS
approved

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Last modified February 21 22:50 EST 2024. Contains 370239 sequences. (Running on oeis4.)