OFFSET
0,3
FORMULA
From Vaclav Kotesovec, Jun 25 2019: (Start)
a(n) ~ c * d^n, where
d = 2.124927028900893046638236231387101475346473032396641627320401...
c = 0.386397654364351443933577245182777062935616240164642598839093... (End)
From Peter Bala, Dec 18 2020
Conjectural g.f.: 1/(2 - (1 + x)/(1 - x^2/(2 - (1 + x^3)/(1 - x^4/(2 - (1 + x^5)/(1 - x^6/(2 - ... ))))))).
More generally it appears that 1/(1 - t*x*(1 + u*x)/(1 - t*x^2*(1 + u*x^2)/(1 - t*x^3*(1 + u*x^3)/(1 - t*x^4*(1 + u*x^4)/(1 - ... ))))) = 1/(1 + u - (u + t*x)/(1 - t*x^2/(1 + u - (u + t*x^3)/(1 - t*x^4/(1 + u - (u + t*x^5)/(1 - ... )))))). (End)
MATHEMATICA
nmax = 33; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^k (1 + x^k), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jun 21 2019
STATUS
approved