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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
1, 1, 1, 1, 2, 3, 4, 6, 10, 15, 22, 34, 53, 80, 121, 187, 287, 436, 666, 1023, 1564, 2386, 3652, 5593, 8548, 13065, 19995, 30590, 46767, 71524, 109425, 167361, 255934, 391466, 598795, 915805, 1400649, 2142358, 3276767, 5011632, 7665186, 11724011, 17931702, 27426003 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

FORMULA

a(n) ~ c * d^n, where d = 1.52948673740109160123259225872298170871226757805081837... and c = 0.3181991399535991335364627230448471420031275308618... - Vaclav Kotesovec, Aug 25 2017

EXAMPLE

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 +...

MATHEMATICA

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 *)

PROG

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

{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)}

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

CROSSREFS

Cf. A206741.

Sequence in context: A073028 A147788 A104977 * A221992 A221993 A221994

Adjacent sequences:  A206739 A206740 A206741 * A206743 A206744 A206745

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 12 2012

STATUS

approved

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Last modified October 5 23:01 EDT 2022. Contains 357261 sequences. (Running on oeis4.)