|
| |
|
|
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
|
| |
|
|
