A088355 G.f.: A(x) = 1/(1-x - x/(1-x - x^2/(1-x - x^3/(1-x - x^4/(1-x - x^5/(...)))))), a continued fraction.

1, 2, 5, 14, 41, 122, 366, 1103, 3332, 10078, 30503, 92360, 279722, 847283, 2566640, 7775383, 23555412, 71361969, 216195801, 654983362, 1984334264, 6011741892, 18213205238, 55178866432, 167170395758, 506461095121, 1534379837420, 4648573702811, 14083369899731, 42667133594949

Offset: 0

Author

Paul D. Hanna, Sep 26 2003

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Programs

Mathematica

nmax = 40; CoefficientList[Series[1/Fold[(1 - x - #2/#1) &, 1, Reverse[x^Range[nmax]]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 24 2017 *)

PARI

N = 66;  q = 'q + O('q^N);
G(k) = if(k>N, 1, 1/( 1 - q - q^(k+1)*G(k+1)) );
gf = G(0); Vec(gf) \\ Joerg Arndt, Jun 29 2013

Formula

a(n) ~ c * d^n, where d = 3.0296112619721892426435033662444766469370800620363379560921091791758304730314... and c = 0.46759853331494118178113003272909690207439354761370218749894486984354... - Vaclav Kotesovec, Sep 24 2017

Extensions

Added more terms, Joerg Arndt, Jun 29 2013