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A089089 Convoluted convolved Fibonacci numbers G_j^(2). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 05 2003
EXTENSIONS
Edited by Emeric Deutsch, Mar 06 2004
STATUS
approved

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Last modified May 22 02:24 EDT 2024. Contains 372741 sequences. (Running on oeis4.)