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A072810 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..33.

FORMULA

G.f.: 1/A(x) = (1-x) + sum_{n=2..inf} mu(n)x^n.

EXAMPLE

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.

CROSSREFS

Sequence in context: A054169 A287185 A065491 * A167606 A065455 A220842

Adjacent sequences:  A072807 A072808 A072809 * A072811 A072812 A072813

KEYWORD

easy,nonn

AUTHOR

Paul D. Hanna, Aug 09 2002

EXTENSIONS

Corrected by Franklin T. Adams-Watters, Oct 25 2006

STATUS

approved

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Last modified August 14 01:40 EDT 2020. Contains 336473 sequences. (Running on oeis4.)