A089089 Convoluted convolved Fibonacci numbers G_j^(2).

0, 1, 2, 5, 9, 19, 34, 65, 115, 210, 368, 654, 1136, 1985, 3422, 5911, 10125, 17345, 29550, 50305, 85311, 144516, 244128, 411900, 693496, 1166209, 1957842, 3283145, 5497985, 9197455, 15368386, 25655489, 42785859, 71293590, 118692688, 197452746, 328223544

Offset

1,3

Links

Table of n, a(n) for n=1..37.

A. R. Ashrafi, J. Azarija, K. Fathalikhani, S. Klavzar, et al., Orbits of Fibonacci and Lucas cubes, dihedral transformations, and asymmetric strings, 2014.

A. R. Ashrafi, J. Azarija, K. Fathalikhani, S. Klavzar and M. Petkovsek, Vertex and edge orbits of Fibonacci and Lucas cubes, 2014; See Table 2.

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

Index entries for linear recurrences with constant coefficients, signature (2,2,-4,-1,0,0,2,1).

Formula

G.f.: (x/2)*(1/(1 - x - x^2)^2 - 1/(1 - x^2 - x^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(2, j), j=1..40);

Mathematica

CoefficientList[Series[(1/2) (1/(1 - x - x^2)^2 - 1/(1 - x^2 - x^4)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 27 2015 *)

Crossrefs

Sequence in context: A085410 A073118 A048082 * A369854 A014495 A056326

Adjacent sequences: A089086 A089087 A089088 * A089090 A089091 A089092

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved