A296201 Expansion of 1/(1 - x/(1 - x/(1 - x^2/(1 - x/(1 - x^3/(1 - x/(1 - x^4/(1 - ...)))))))), a continued fraction.

1, 1, 2, 4, 9, 21, 50, 120, 290, 704, 1714, 4181, 10212, 24965, 61070, 149458, 365888, 895932, 2194178, 5374262, 13164426, 32248616, 79002180, 193544446, 474168003, 1161691893, 2846131055, 6973047572, 17084140245, 41856763371, 102550935614, 251254982356, 615588531011, 1508227753087, 3695249380509

Offset: 0

Author

Ilya Gutkovskiy, Dec 07 2017

Keywords

• nonn

Crossrefs

Cf. A004148, A005169, A023432, A088354, A088355, A296202.

Programs

Mathematica

nmax = 34; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(1 + k (1 + (-1)^k)/4), 1, {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

a(n) ~ c * d^n, where d = 2.450066970712861209761227155593662591019701927336233634485900133440192... and c = 0.21656595617747023258115906735909123622190252865232858964820650877171... - Vaclav Kotesovec, Sep 18 2021