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A089109 Convoluted convolved Fibonacci numbers G_5^(r). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
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
MAPLE
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);
MATHEMATICA
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}];
Array[a, terms] (* Jean-François Alcover, Dec 09 2017, from Maple *)
CROSSREFS
Sequence in context: A182388 A080335 A351837 * A100449 A146284 A175543
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 05 2003
EXTENSIONS
Edited by Emeric Deutsch, Mar 06 2004
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)