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A223202
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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
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7
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..364
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FORMULA
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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]
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin Mar 18 2013
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STATUS
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approved
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