A294410 Expansion of 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 2*x^2/(1 - 3*x^3/(1 - 3*x^3/(1 - ...))))))), a continued fraction.

1, 1, 2, 4, 10, 24, 64, 164, 440, 1164, 3128, 8368, 22552, 60624, 163528, 440768, 1189616, 3210000, 8667296, 23400304, 63196192, 170668608, 460972768, 1245085184, 3363190688, 9084616128, 24540062528, 66289885504, 179071151872, 483733046208, 1306740302848, 3529993576448, 9535868752256

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Formula

a(n) ~ c * d^n, where d = 2.7014053577058965980816004348205865476643047417470551135866... and c = 0.1473934094237780704912896884660893313026695094814554837... - Vaclav Kotesovec, Sep 16 2021

Mathematica

nmax = 32; CoefficientList[Series[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2] x^Floor[(k + 1)/2], 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000142, A006958, A088357.

Sequence in context: A303840 A132220 A007874 * A121704 A049144 A354733

Adjacent sequences: A294407 A294408 A294409 * A294411 A294412 A294413

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 30 2017

Status

approved