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A329311
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a(n) is the product of the numbers k such that a(n-2*k) = a(n-k) and 0 < n-2*k < n-k < n.
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2
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1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 8, 10, 90, 42, 42, 56, 56, 72, 9, 10, 1, 1, 1, 1, 2, 2, 3, 8, 1, 1, 1, 11, 24, 780, 1092, 7644, 11760, 11760, 311040, 2736, 64600, 420, 420, 462, 157080, 10626, 483, 210672, 20, 420, 462, 462, 506, 23, 624, 27, 5292, 45472, 812
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OFFSET
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1,5
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COMMENTS
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This sequence has fractal features; apparently, for any k > 0, the first k terms are repeated later (see illustration in Links section).
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LINKS
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EXAMPLE
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The first terms, alongside the corresponding k's, are:
n a(n) k's
--- ------- ---------
1 1 {}
2 1 {}
3 1 {1}
4 1 {1}
5 2 {1, 2}
6 2 {2}
7 3 {1, 3}
8 1 {}
9 1 {}
10 1 {1}
11 1 {1}
12 8 {1, 2, 4}
13 10 {2, 5}
14 90 {3, 5, 6}
15 42 {6, 7}
16 42 {6, 7}
17 56 {1, 7, 8}
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PROG
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(PARI) for (n=1, #(a=vector(60)), print1 (a[n] = prod(k=1, (n-1)\2, if (a[n-k]==a[n-2*k], k, 1)) ", "))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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