A089109 Convoluted convolved Fibonacci numbers G_5^(r).

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

Offset

1,1

Links

Table of n, a(n) for n=1..48.

P. Moree, Convoluted convolved Fibonacci numbers

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 A374672

Adjacent sequences: A089106 A089107 A089108 * A089110 A089111 A089112

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved