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Search: id:A073777
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| 1, 2, 5, 10, 22, 42, 85, 162, 314, 588, 1113, 2066, 3847, 7080, 13036, 23824, 43504, 79048, 143441, 249376, 468313, 843352, 1516515, 2721470, 296550, 510886, 880580, 1517226, 2614889, 4505745, 7765094, 13380640, 23059193, 39735969
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OFFSET
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0,2
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COMMENT
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Recurrence relation involves the convolution of the Moebius function (A068341).
Radius of convergence of A(x) is r=0.5802946238073267... Related limits are limit_{n->inf} a(n) r^n /n = 0.406...(?) and limit_{n->inf} a(n+1)/a(n) = 1.723262561763844... This sequence is the convolution of A073776.
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FORMULA
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G.f.: A(x)= x/sum(mu(n)*x^n, n=1..inf)^2, A(0)=1, where mu(n)=Moebius function; a(n) = sum(-A068341(k+1)*a(n-k), k=1..n), a(0)=1.
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EXAMPLE
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a(4) = -A068341(2)a(3) -A068341(3)a(2) -A068341(4)a(1) -A068341(5)a(0) = 2*10 +1*5 -2*2 +1*1 = 22. A068341 begins {1,-2,-1,2,-1,4,-2,0,3,...}.
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CROSSREFS
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Cf. A073776, A068341, A070965, A008683.
Sequence in context: A034456 A002512 A097096 this_sequence A110744 A026633 A093370
Adjacent sequences: A073774 A073775 A073776 this_sequence A073778 A073779 A073780
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 10 2002
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