A089116 Convoluted convolved Fibonacci numbers G_j^(3).

0, 1, 3, 7, 17, 37, 77, 158, 314, 611, 1174, 2222, 4156, 7703, 14149, 25790, 46703, 84059, 150476, 268076, 475460, 839873, 1478140, 2592620, 4533157, 7903261, 13741783, 23833789, 41241117, 71206561, 122693568, 211003818, 362221854

Offset

1,3

Links

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

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

Index entries for linear recurrences with constant coefficients, signature (3,0,-4,-3,3,7,-3,-3,4,0,-3,-1)

Formula

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

a(n) = +3*a(n-1) -4*a(n-3) -3*a(n-4) +3*a(n-5) +7*a(n-6) -3*a(n-7) -3*a(n-8) +4*a(n-9) -3*a(n-11) -a(n-12). - R. J. Mathar, Jan 25 2011

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

Mathematica

gf = (z/3) (1/(1 - z - z^2)^3 - 1/(1 - z^3 - z^6));
CoefficientList[gf + O[z]^40, z] // Rest (* Jean-François Alcover, Dec 01 2017 *)

Crossrefs

Sequence in context: A221792 A354124 A089099 * A244629 A065545 A110930

Adjacent sequences: A089113 A089114 A089115 * A089117 A089118 A089119

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved