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A206742 G.f.: 1/(1 - x/(1 - x^3/(1 - x^4/(1 - x^7/(1 - x^11/(1 - x^18/(1 -...- x^Lucas(n)/(1 -...)))))))), a continued fraction. 5

%I #16 Aug 25 2017 03:53:06

%S 1,1,1,1,2,3,4,6,10,15,22,34,53,80,121,187,287,436,666,1023,1564,2386,

%T 3652,5593,8548,13065,19995,30590,46767,71524,109425,167361,255934,

%U 391466,598795,915805,1400649,2142358,3276767,5011632,7665186,11724011,17931702,27426003

%N G.f.: 1/(1 - x/(1 - x^3/(1 - x^4/(1 - x^7/(1 - x^11/(1 - x^18/(1 -...- x^Lucas(n)/(1 -...)))))))), a continued fraction.

%H Vaclav Kotesovec, <a href="/A206742/b206742.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) ~ c * d^n, where d = 1.52948673740109160123259225872298170871226757805081837... and c = 0.3181991399535991335364627230448471420031275308618... - _Vaclav Kotesovec_, Aug 25 2017

%e G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 10*x^8 +...

%t nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(LucasL[Range[nmax + 1]])]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 25 2017 *)

%o (PARI) {Lucas(n)=polcoeff(x*(1+2*x)/(1-x-x^2+x*O(x^n)),n)}

%o {a(n)=local(CF=1+x*O(x^n),M=ceil(log(n+1)/log(1.6))); for(k=0, M, CF=1/(1-x^Lucas(M-k+1)*CF)); polcoeff(CF, n, x)}

%o for(n=0,55,print1(a(n),", "))

%Y Cf. A206741.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Feb 12 2012

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)