A292800 Expansion of 1/(1 - x - x^3/(1 - x^5 - x^7/(1 - x^9 - x^11/(1 - x^13 - x^15/(1 - ...))))), a continued fraction.

1, 1, 1, 2, 3, 4, 6, 9, 14, 21, 32, 49, 74, 113, 172, 262, 399, 607, 925, 1409, 2146, 3269, 4979, 7584, 11552, 17596, 26803, 40826, 62187, 94725, 144287, 219782, 334776, 509939, 776752, 1183167, 1802230, 2745201, 4181558, 6369454, 9702111, 14778499, 22510979, 34289286, 52230301, 79558503

Offset

0,4

Links

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

Formula

a(n) ~ c * d^n, where d = 1.523225094265657459818421502249017511338863636291677936060889201502867407829... and c = 0.47457266943464547141454496057039844482970984208404015222172896259335... - Vaclav Kotesovec, Sep 24 2017

Mathematica

nmax = 45; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x^(4 k - 1), 1 - x^(4 k + 1), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A088352, A292802.

Sequence in context: A355910 A143951 A328262 * A214041 A058355 A179041

Adjacent sequences: A292797 A292798 A292799 * A292801 A292802 A292803

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2017

Status

approved