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A089117 Convoluted convolved Fibonacci numbers G_j^(4). 2
0, 1, 3, 10, 25, 64, 146, 331, 710, 1505, 3091, 6272, 12473, 24540, 47610, 91527, 174138, 328768, 615720, 1145650, 2117884, 3893630, 7119978, 12958400, 23478010, 42364427, 76148353, 136389128, 243467595, 433263360, 768749914, 1360269093 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..32.

P. Moree, Convoluted convolved Fibonacci numbers

Index entries for linear recurrences with constant coefficients, signature (4,0,-16,10,20,-12,-4,-7,-12,12,12,2,0,-4,-4,-1).

FORMULA

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

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

MATHEMATICA

LinearRecurrence[{4, 0, -16, 10, 20, -12, -4, -7, -12, 12, 12, 2, 0, -4, -4, -1}, {0, 1, 3, 10, 25, 64, 146, 331, 710, 1505, 3091, 6272, 12473, 24540, 47610, 91527}, 40]

(* Ray Chandler, Jul 15 2015 *)

CROSSREFS

Sequence in context: A262380 A005674 A089100 * A176610 A026965 A130783

Adjacent sequences:  A089114 A089115 A089116 * A089118 A089119 A089120

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2003

EXTENSIONS

Edited by Emeric Deutsch, Mar 06 2004

STATUS

approved

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Last modified October 26 00:28 EDT 2020. Contains 338026 sequences. (Running on oeis4.)