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%I #22 Nov 17 2017 12:05:19
%S 1,-1,1,-1,2,-3,4,-6,8,-11,16,-22,31,-44,61,-85,119,-166,232,-325,454,
%T -634,886,-1237,1728,-2415,3373,-4712,6583,-9194,12843,-17941,25060,
%U -35006,48899,-68303,95409,-133272,186159,-260036,363230,-507373,708720,-989969,1382827,-1931590
%N Expansion of 1/(1 + x/(1 + x^3/(1 + x^4/(1 + x^7/(1 + x^11/(1 + ... + x^Lucas(k)/(1 + ...))))))), a continued fraction.
%F G.f.: 1/(1 + x/(1 + x^3/(1 + x^4/(1 + x^7/(1 + x^11/(1 + ... + x^A000204(k)/(1 + ...))))))), a continued fraction.
%t nmax = 45; CoefficientList[Series[1/(1 + ContinuedFractionK[x^LucasL[k], 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000204, A007325, A206741, A206742, A206743, A279586.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Nov 16 2017
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