A089096 Convoluted convolved Fibonacci numbers G_j^(9).

0, 1, 6, 28, 115, 418, 1396, 4367, 12925, 36542, 99385, 261365, 667501, 1661325, 4041025, 9629631, 22526515, 51820065, 117401263, 262291425, 578530315, 1261055274, 2718900535, 5802916275, 12268722487, 25711496512, 53441431933, 110223868969, 225695796260

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

P. Moree, Convoluted convolved Fibonacci numbers

Formula

G.f.: (z/9)[1/(1-z-z^2)^9-1/(1-z^3-z^6)^3].

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

Mathematica

CoefficientList[(z/9)(1/(1-z-z^2)^9 - 1/(1-z^3-z^6)^3) + O[z]^28, z] // Rest (* Jean-François Alcover, Dec 09 2017 *)

Prog

(PARI) concat(0, Vec(x^2*(1 - x)^2*(1 + x)^2*(1 - 3*x + 3*x^2 + 4*x^3 - 9*x^4 - 3*x^5 + 11*x^6 + 3*x^7 - 9*x^8 - 4*x^9 + 3*x^10 + 3*x^11 + x^12) / ((1 - x - x^2)^9*(1 - x^3 - x^6)^3) + O(x^40))) \\ Colin Barker, Dec 09 2017

Crossrefs

Sequence in context: A055220 A027106 A309717 * A229587 A230492 A026014

Adjacent sequences: A089093 A089094 A089095 * A089097 A089098 A089099

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved