A223202 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 vertical neighbor moves across a corresponding cube edge

1, 4, 4, 16, 48, 16, 64, 576, 576, 64, 256, 6912, 20992, 6912, 256, 1024, 82944, 765952, 765952, 82944, 1024, 4096, 995328, 27951104, 85327872, 27951104, 995328, 4096, 16384, 11943936, 1020002304, 9515827200, 9515827200, 1020002304, 11943936

Offset

1,2

Comments

Table starts

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

....4.....48........576..........6912............82944..............995328

...16....576......20992........765952.........27951104..........1020002304

...64...6912.....765952......85327872.......9515827200.......1061444124672

..256..82944...27951104....9515827200....3249109204992....1110327429169152

.1024.995328.1020002304.1061444124672.1110327429169152.1163614255186968576

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

k=5: a(n) = 512*a(n-1) -66560*a(n-2) +3014656*a(n-3) -50331648*a(n-4) +268435456*a(n-5)

k=6: [order 7]

k=7: [order 13]

Example

Some solutions for n=3 k=4
..0..2..4..2....0..1..5..4....0..3..4..2....0..2..0..4....0..2..0..3
..3..1..2..5....3..5..3..0....3..1..3..5....3..5..2..0....3..5..2..5
..0..3..1..2....0..2..0..2....0..3..5..4....1..3..5..2....1..2..1..2
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

Crossrefs

Column 1 is A000302(n-1)

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

Sequence in context: A219398 A222104 A257613 * A298448 A222144 A342817

Adjacent sequences: A223199 A223200 A223201 * A223203 A223204 A223205

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved