A089092 Convoluted convolved Fibonacci numbers G_j^(5).

0, 1, 4, 13, 38, 102, 259, 626, 1457, 3287, 7224, 15529, 32746, 67907, 138767, 279895, 558020, 1100930, 2151610, 4169060, 8015125, 15299090, 29010460, 54676270, 102469595, 191037405, 354426478, 654575187, 1203777114, 2204962989

Offset

1,3

Links

Table of n, a(n) for n=1..30.

P. Moree, Convoluted convolved Fibonacci numbers

Formula

G.f.: (z/5)[1/(1-z-z^2)^5-1/(1-z^5-z^10)].

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(5, j), j=1..40);

Mathematica

f[z_] := 1/(1 - z - z^2);
m[r_] := (z/r)*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}];
CoefficientList[m[5] + O[z]^31, z] // Rest (* Jean-François Alcover, Nov 28 2017, from Maple *)

Crossrefs

Sequence in context: A145128 A357286 A277974 * A181527 A049611 A084851

Adjacent sequences: A089089 A089090 A089091 * A089093 A089094 A089095

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved