A089095 Convoluted convolved Fibonacci numbers G_j^(8).

0, 1, 5, 24, 89, 309, 967, 2871, 8043, 21659, 56123, 141115, 345027, 824010, 1926052, 4418205, 9962470, 22121895, 48435795, 104703830, 223690751, 472762785, 989226119, 2050830465, 4215262759, 8594839851, 17393852163, 34954808319, 69784283227, 138458338326

Offset

1,3

Links

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

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

Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.

Formula

G.f.: (z/8)[1/(1-z-z^2)^8-1/(1-z^2-z^4)^4].

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

Mathematica

(1/8)(1/(1-z-z^2)^8-1/(1-z^2-z^4)^4) + O[z]^30 // CoefficientList[#, z]& (* Jean-François Alcover, Mar 27 2018 *)

Crossrefs

Sequence in context: A334459 A270682 A272420 * A220316 A220339 A158499

Adjacent sequences: A089092 A089093 A089094 * A089096 A089097 A089098

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved