A089117 - OEIS

%I #11 Jul 15 2015 21:12:17

%S 0,1,3,10,25,64,146,331,710,1505,3091,6272,12473,24540,47610,91527,

%T 174138,328768,615720,1145650,2117884,3893630,7119978,12958400,

%U 23478010,42364427,76148353,136389128,243467595,433263360,768749914,1360269093

%N Convoluted convolved Fibonacci numbers G_j^(4).

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

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-16,10,20,-12,-4,-7,-12,12,12,2,0,-4,-4,-1).

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

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

%t 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]

%t (* _Ray Chandler_, Jul 15 2015 *)

%K nonn

%O 1,3

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

%E Edited by _Emeric Deutsch_, Mar 06 2004