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A089109
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Convoluted convolved Fibonacci numbers G_5^(r).
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0
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5, 9, 17, 25, 38, 51, 70, 89, 115, 141, 175, 209, 252, 295, 348, 401, 465, 529, 605, 681, 770, 859, 962, 1065, 1183, 1301, 1435, 1569, 1720, 1871, 2040, 2209, 2397, 2585, 2793, 3001, 3230, 3459, 3710, 3961, 4235, 4509, 4807, 5105, 5428, 5751, 6100, 6449
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OFFSET
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1,1
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LINKS
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FORMULA
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Conjecture: a(n) = (66-18*(-1)^n+(115-3*(-1)^n)*n+36*n^2+2*n^3)/48. G.f.: -x*(x^5-2*x^4-2*x^3+6*x^2+x-5) / ((x-1)^4*(x+1)^2). - Colin Barker, Jul 31 2013
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MAPLE
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with(numtheory): f := z->1/(1-z-z^2): m := proc(r, j) d := divisors(r): W := (1/r)*z*sum(mobius(d[i])*f(z^d[i])^(r/d[i]), i=1..nops(d)): Wser := simplify(series(W, z=0, 80)): coeff(Wser, z^j) end: seq(m(r, 5), r=1..65);
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MATHEMATICA
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terms = 48;
f[z_] := 1/(1 - z - z^2);
a[r_] := SeriesCoefficient[(z/r)*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}], {z, 0, 5}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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