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

Author

N. J. A. Sloane, Dec 05 2003

Keywords

• nonn
• easy

Links

• P. Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO], 2003.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Programs

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 *)

Formula

G.f.: x*(3 - x - 2*x^3 + x^4)/((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

Extensions

Edited by Emeric Deutsch, Mar 06 2004