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A206741 G.f.: 1/(1 - x/(1 - x/(1 - x^2/(1 - x^3/(1 - x^5/(1 - x^8/(1 -...- x^Fibonacci(n)/(1 -...)))))))), a continued fraction. 6
1, 1, 2, 4, 9, 20, 45, 102, 231, 524, 1189, 2698, 6124, 13900, 31551, 71618, 162566, 369013, 837633, 1901368, 4315978, 9796979, 22238489, 50479892, 114585999, 260102617, 590415686, 1340204451, 3042175244, 6905536091, 15675109089, 35581458383, 80767551510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ c * d^n, where d = 2.2699337019511296354569330617166782764872939098477919669570757033487700138... and c = 0.3272015736512679060779796519077970622372291004190408455581585307453... - Vaclav Kotesovec, Aug 25 2017

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 102*x^7 +...

MATHEMATICA

nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(Fibonacci[Range[nmax + 1]])]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 25 2017 *)

PROG

(PARI) {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^fibonacci(M-k+1)*CF)); polcoeff(CF, n, x)}

for(n=0, 50, print1(a(n), ", "))

CROSSREFS

Cf. A206742, A206743.

Sequence in context: A213411 A080135 A227978 * A167750 A343756 A329276

Adjacent sequences:  A206738 A206739 A206740 * A206742 A206743 A206744

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 12 2012

STATUS

approved

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Last modified October 4 08:40 EDT 2022. Contains 357239 sequences. (Running on oeis4.)