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.

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

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: A374763 A147788 A104977 * A221992 A221993 A221994

Adjacent sequences: A206739 A206740 A206741 * A206743 A206744 A206745

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2012

Status

approved