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A223270
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Rolling cube footprints: number of 2 X n 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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1
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6, 48, 576, 6144, 67584, 737280, 8060928, 88080384, 962592768, 10519314432, 114957484032, 1256277934080, 13728862961664, 150031797583872, 1639577995444224, 17917641486237696, 195807627744116736
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 8*a(n-1) + 32*a(n-2).
G.f.: 6*x / (1 - 8*x - 32*x^2).
a(n) = (sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n)) / 4.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..2..0....0..2..1....0..3..4....0..2..4....0..2..0....0..1..2....0..4..2
..5..3..4....4..3..1....4..2..4....1..3..1....1..3..5....2..4..3....0..1..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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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