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A223481
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Rolling icosahedron face footprints: number of 3 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
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1
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400, 243, 2025, 16875, 147825, 1296675, 11374425, 99776475, 875239425, 7677601875, 67347938025, 590776238475, 5182290270225, 45459059955075, 398766959055225, 3497984511586875, 30684326686171425, 269162971152369075
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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) = 9*a(n-1) - 2*a(n-2) for n>4.
Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - Colin Barker, Aug 20 2018
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EXAMPLE
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Some solutions for n=3:
..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6
..3..4..1....0..2..8....3..2..8....0..5..9....0..2..0....3..2..3....6..1..6
..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12
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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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