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A073776
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a(n) = sum(-mu(k+1)*a(n-k),k=1..n), a(0)=1.
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3
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1, 1, 2, 3, 6, 9, 17, 28, 50, 83, 147, 249, 435, 742, 1288, 2207, 3819, 6561, 11333, 19497, 33640, 57915, 99874, 172020, 296550, 510886, 880580, 1517226, 2614889, 4505745, 7765094, 13380640, 23059193, 39735969, 68476885, 118001888
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Recurrence relation involves the Moebius function.
Radius of convergence of A(x) is r=0.5802946238073267... Related limits are limit_{n->inf} a(n) r^n = 0.6303632342... and limit_{n->inf} a(n+1)/a(n) = 1.723262561763844...
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FORMULA
| G.f.: A(x) = x/sum(mu(n)*x^n, n=1..inf), A(0)=1, where mu(n)=Moebius function.
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EXAMPLE
| a(6) = -mu(2)a(5) -mu(3)a(4) -mu(4)a(3) -mu(5)a(2) -mu(6)a(1) -mu(7)a(0) = 9 +6 +0 +2 -1 +1 = 17.
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MATHEMATICA
| a[0] = 1; a[n_] := a[n] = Sum[-MoebiusMu[k + 1]*a[n - k], {k, 1, n}]; Array[a, 35, 0] (* From Jean-François Alcover, Apr 11 2011 *)
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CROSSREFS
| Cf. A073777, A068341, A070965, A008683.
Sequence in context: A048814 A048815 A074045 * A129853 A095982 A095090
Adjacent sequences: A073773 A073774 A073775 * A073777 A073778 A073779
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 10 2002
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