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A223182
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Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.
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1
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125, 320, 2080, 14560, 103520, 738720, 5274720, 37664800, 268947680, 1920431520, 13712917600, 97917648160, 699184991200, 4992559175840, 35649574015840, 254557248560160, 1817676496339680, 12979193733707680, 92678466337073760
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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) = 10*a(n-1) - 25*a(n-2) + 36*a(n-3) - 24*a(n-4) + 4*a(n-5) for n>6.
Empirical g.f.: 5*x*(25 - 186*x + 401*x^2 - 548*x^3 + 280*x^4 - 36*x^5) / ((1 - x)*(1 - 9*x + 16*x^2 - 20*x^3 + 4*x^4)). - Colin Barker, Aug 17 2018
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EXAMPLE
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Some solutions for n=3:
..0..5..7.11....0..5.10.11....0..5..7..0....0..6..2..0....0..5.10.11
..7.11..3..7....7.11..5.10....7.11..5..7....2..0..1..7....7.11..9.10
..5..7..1..3....5..7.11..5....3..7..0..5....1..7..0..1....5.10..4..9
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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