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A223333
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Rolling cube footprints: number of 4 X n 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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512, 2187, 83349, 3176523, 121264857, 4630596579, 176834343105, 6753068175483, 257891143282857, 9848539671395859, 376103406869296785, 14362918587487614123, 548501892736263190137, 20946601106278812695619
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 48*a(n-1) - 402*a(n-2) + 1064*a(n-3) - 789*a(n-4) for n>7.
Empirical g.f.: x*(512 - 22389*x + 184197*x^2 - 489823*x^3 + 375051*x^4 - 112104*x^5 + 121716*x^6) / ((1 - 3*x)*(1 - 45*x + 267*x^2 - 263*x^3)). - Colin Barker, Aug 19 2018
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EXAMPLE
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Some solutions for n=3:
..0..2..0....0..1..0....0..2..3....0..1..0....0..1..3....0..4..5....0..1..0
..6..2..3....0..1..0....6..7..3....0..2..0....3..1..0....5..4..5....5..4..5
..6..7..5....0..1..3....3..7..6....3..1..3....5..1..0....0..1..0....0..1..0
..3..1..3....5..1..0....6..2..6....0..1..0....3..1..5....3..2..6....0..4..5
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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