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A223329
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Rolling cube footprints: number of n X 6 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.
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1
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243, 64827, 17324685, 4630596579, 1237689159021, 330815891296611, 88422165323034669, 23633929115222765283, 6316997592145707860589, 1688439462802532886238947, 451294745322310558858483245
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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) = 282*a(n-1) - 3969*a(n-2) + 9604*a(n-3).
Empirical g.f.: 27*x*(9 - 137*x + 294*x^2) / (1 - 282*x + 3969*x^2 - 9604*x^3). - Colin Barker, Aug 19 2018
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EXAMPLE
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Some solutions for n=3:
..0..4..0..4..6..2....0..4..0..1..0..1....0..4..6..7..5..1....0..4..0..1..5..4
..0..4..0..2..0..2....0..4..5..4..5..4....0..4..5..4..0..1....0..4..5..4..6..7
..0..4..6..4..0..2....0..4..5..4..5..4....0..4..5..4..0..2....0..4..5..4..5..7
Vertex neighbors:
0 -> 1 2 4
1 -> 0 3 5
2 -> 0 3 6
3 -> 1 2 7
4 -> 0 5 6
5 -> 1 4 7
6 -> 2 4 7
7 -> 3 5 6
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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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