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.

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

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