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A089108 Convoluted convolved Fibonacci numbers G_4^(r).

%I A089108 #20 Jan 05 2025 13:36:24
%S A089108 3,5,7,10,13,16,20,24,28,33,38,43,49,55,61,68,75,82,90,98,106,115,124,
%T A089108 133,143,153,163,174,185,196,208,220,232,245,258,271,285,299,313,328,
%U A089108 343,358,374,390,406,423,440,457,475,493,511,530,549,568,588,608,628
%N A089108 Convoluted convolved Fibonacci numbers G_4^(r).
%H A089108 P. Moree, <a href="https://arxiv.org/abs/math/0311205">Convoluted convolved Fibonacci numbers</a>, arXiv:math/0311205 [math.CO], 2003.
%H A089108 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A089108 G.f.: x*(3 - x - 2*x^3 + x^4)/((1 - x^3)*(1 - x)^2).
%F A089108 9*a(n) = 11 +27*n/2 +3*n^2/2 -A099837(n+3). - _R. J. Mathar_, Jan 09 2024
%p A089108 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);
%t A089108 LinearRecurrence[{2, -1, 1, -2, 1}, {3, 5, 7, 10, 13}, 60] (* _Jean-François Alcover_, Nov 28 2017 *)
%K A089108 nonn,easy
%O A089108 1,1
%A A089108 _N. J. A. Sloane_, Dec 05 2003
%E A089108 Edited by _Emeric Deutsch_, Mar 06 2004