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Convoluted convolved Fibonacci numbers G_4^(r).
1

%I #15 Jan 09 2024 12:00:38

%S 3,5,7,10,13,16,20,24,28,33,38,43,49,55,61,68,75,82,90,98,106,115,124,

%T 133,143,153,163,174,185,196,208,220,232,245,258,271,285,299,313,328,

%U 343,358,374,390,406,423,440,457,475,493,511,530,549,568,588,608,628

%N Convoluted convolved Fibonacci numbers G_4^(r).

%H P. Moree, <a href="https://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

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

%F 9*a(n) = 11 +27*n/2 +3*n^2/2 -A099837(n+3). - _R. J. Mathar_, Jan 09 2024

%p 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 LinearRecurrence[{2, -1, 1, -2, 1}, {3, 5, 7, 10, 13}, 60] (* _Jean-François Alcover_, Nov 28 2017 *)

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Dec 05 2003

%E Edited by _Emeric Deutsch_, Mar 06 2004