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Search: id:A072810
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| A072810 |
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a(0)=1, a(n) = a(n-1) - sum_{k=2..n} mu(k)a(n-k), where mu(k) is the Moebius function of k. |
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1
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| 1, 1, 2, 4, 7, 14, 25, 48, 90, 168, 316, 592, 1112, 2086, 3913, 7342, 13775, 25845, 48490, 90978, 170694, 320257, 600867, 1127352, 2115147, 3968453, 7445640, 13969562, 26209794, 49175002, 92262491, 173103549, 324778120, 609351037
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OFFSET
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0,3
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COMMENT
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The radius of convergence of the series A(x) is r=0.5329901818866726, where r is a solution to (1-r) + sum_{n=2..inf} mu(n)r^n = 0. Related limits are limit_{n->inf} a(n) r^n = 0.5842536738793409 and limit_{n->inf} a(n+1)/a(n) = 1.8762071685077034.
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FORMULA
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G.f.: 1/A(x) = (1-x) + sum_{n=2..inf} mu(n)x^n.
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EXAMPLE
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a(6)=a(5)-mu(2)a(4)-mu(3)a(3)-mu(4)a(2)-mu(5)a(1)-mu(6)a(0)=14+7+4+0+1-1=25.
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CROSSREFS
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Sequence in context: A000076 A054169 A065491 this_sequence A167606 A065455 A026010
Adjacent sequences: A072807 A072808 A072809 this_sequence A072811 A072812 A072813
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2002
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EXTENSIONS
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Corrected by Franklin T. Adams-Watters, Oct 25 2006
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