A089108 Convoluted convolved Fibonacci numbers G_4^(r).

3, 5, 7, 10, 13, 16, 20, 24, 28, 33, 38, 43, 49, 55, 61, 68, 75, 82, 90, 98, 106, 115, 124, 133, 143, 153, 163, 174, 185, 196, 208, 220, 232, 245, 258, 271, 285, 299, 313, 328, 343, 358, 374, 390, 406, 423, 440, 457, 475, 493, 511, 530, 549, 568, 588, 608, 628

Offset

1,1

Links

Table of n, a(n) for n=1..57.

P. Moree, Convoluted convolved Fibonacci numbers

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

Formula

G.f.: x(x^4-2x^3-x+3)/[(1-x^3)(1-x)^2].

9*a(n) = 11 +27*n/2 +3*n^2/2 -A099837(n+3). - R. J. Mathar, Jan 09 2024

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(r, 4), r=1..60);

Mathematica

LinearRecurrence[{2, -1, 1, -2, 1}, {3, 5, 7, 10, 13}, 60] (* Jean-François Alcover, Nov 28 2017 *)

Crossrefs

Sequence in context: A001768 A327672 A329815 * A186355 A029899 A072166

Adjacent sequences: A089105 A089106 A089107 * A089109 A089110 A089111

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 05 2003

Extensions

Edited by Emeric Deutsch, Mar 06 2004

Status

approved