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

0,3

Links

Table of n, a(n) for n=0..34.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A018905 A024537 A171842 * A027826 A261664 A355043

Adjacent sequences: A296198 A296199 A296200 * A296202 A296203 A296204

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 07 2017

Status

approved