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%I #18 Dec 01 2017 09:38:45
%S 0,1,3,7,17,37,77,158,314,611,1174,2222,4156,7703,14149,25790,46703,
%T 84059,150476,268076,475460,839873,1478140,2592620,4533157,7903261,
%U 13741783,23833789,41241117,71206561,122693568,211003818,362221854
%N Convoluted convolved Fibonacci numbers G_j^(3).
%H P. Moree, <a href="https://arxiv.org/abs/math/0311205">Convoluted convolved Fibonacci numbers</a>, arXiv:math/0311205 [math.CO], 2003.
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-4,-3,3,7,-3,-3,4,0,-3,-1)
%F G.f.: (z/3)[1/(1-z-z^2)^3-1/(1-z^3-z^6)].
%F a(n) = +3*a(n-1) -4*a(n-3) -3*a(n-4) +3*a(n-5) +7*a(n-6) -3*a(n-7) -3*a(n-8) +4*a(n-9) -3*a(n-11) -a(n-12). - _R. J. Mathar_, Jan 25 2011
%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(3,j),j=1..40);
%t gf = (z/3) (1/(1 - z - z^2)^3 - 1/(1 - z^3 - z^6));
%t CoefficientList[gf + O[z]^40, z] // Rest (* _Jean-François Alcover_, Dec 01 2017 *)
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Dec 05 2003
%E Edited by _Emeric Deutsch_, Mar 06 2004
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