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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 20:05 EST 2021. Contains 349395 sequences. (Running on oeis4.)