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A223269
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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, diagonal or antidiagonal neighbor moves across a corresponding cube edge
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12
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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
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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
....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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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Column 2 is 4*12^(n-1)
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KEYWORD
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AUTHOR
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STATUS
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approved
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