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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2012
STATUS
approved