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

Author

R. H. Hardin Mar 18 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302(n-1)

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

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) [phone]*a(n-5)

k=6: [order 7]

k=7: [order 13]