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.

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

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