A089115 Convoluted convolved Fibonacci numbers G_8^(r).

21, 65, 158, 331, 626, 1098, 1817, 2871, 4367, 6435, 9230, 12935, 17764, 23965, 31824, 41667, 53865, 68837, 87054, 109043, 135391, 166750, 203840, 247455, 298467, 357831, 426590, 505880, 596936, 701096, 819808, 954635, 1107261

Offset

1,1

Links

Table of n, a(n) for n=1..33.

P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.

Formula

Empirical g.f.: -x*(4*x^12 -24*x^11 +60*x^10 -80*x^9 +59*x^8 -20*x^7 -4*x^5 +25*x^4 -62*x^3 +83*x^2 -61*x +21) / ((x -1)^7*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - 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, 8), r=1..50);

Mathematica

f[z_] := 1/(1 - z - z^2);
m[r_] := (1/r)*z*Sum[MoebiusMu[d]*f[z^d]^(r/d), {d, Divisors[r]}];
Table[SeriesCoefficient[m[r], {z, 0, 8}], {r, 1, 33}] (* Jean-François Alcover, Dec 06 2017, from Maple *)

Crossrefs

Sequence in context: A020211 A014641 A259677 * A259244 A020309 A048713

Adjacent sequences: A089112 A089113 A089114 * A089116 A089117 A089118

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved