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A060481
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Number of orbits of length n in a map whose periodic points come from A059991.
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0
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1, 0, 1, 0, 3, 2, 9, 0, 28, 24, 93, 20, 315, 288, 1091, 0, 3855, 3626, 13797, 3264, 49929, 47616, 182361, 2720, 671088, 645120, 2485504, 599040, 9256395, 8947294, 34636833, 0, 130150493, 126320640, 490853403, 119302820, 1857283155, 1808400384, 7048151355
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OFFSET
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1,5
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COMMENTS
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Terms a(2)-a(20) of this sequence and sequence A000048 appear on p. 311 of Sommerville (1909) in the context of sequences of "evolutes" of cyclic compositions of positive integers.
Algebraically, it is easy to prove that this sequence and sequence A000048 have the same odd-indexed terms. (End)
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LINKS
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FORMULA
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If b(n) is the n-th term of A059991, then a(n) = (1/n)* Sum_{d|n} mu(d)*b(n/d). [Corrected by Petros Hadjicostas, Jan 14 2018]
a(2*n-1) = A000048(2*n-1) for n >= 1.
a(2^m) = 0 for m >= 1.
G.f.: If B(x) is the g.f. of the sequence b(n) = A059991(n) and C(x) = integrate(B(y)/y, y = 0..x), then the g.f. of the current sequence is A(x) = Sum_{n>=1} (mu(n)/n)*C(x^n). (End)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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