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A223234
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Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.
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1
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12, 65, 785, 7445, 75665, 753005, 7540985, 75377045, 753868865, 7538393405, 75384819785, 753845540645, 7538463378065, 75384609865805, 753846170402585, 7538461488792245, 75384615533623265, 753846153399130205
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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) = 7*a(n-1) + 30*a(n-2) for n>3.
G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).
a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0
..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..4
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10
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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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