login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235349 Series reversion of x*(1-x-2*x^2)/(1-x). 2
0, 1, 0, 2, 2, 14, 30, 146, 434, 1862, 6470, 26586, 99946, 406366, 1593774, 6492450, 26100578, 106979894, 436906902, 1803472874, 7446478746, 30945624910, 128821054846, 538584390834, 2256485249682, 9483898177574 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Derived turbulence series from A235347.

LINKS

Fung Lam, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: ( exp(4*Pi*i/3)*u + exp(2*Pi*i/3)*v - 1/6 )/x, where i=sqrt(-1),

u = 1/6*(-10-63*x+3*sqrt(-24*x^3+357*x^2+42*x-27))^(1/3), and

v = 1/6*(-10-63*x-3*sqrt(-24*x^3+357*x^2+42*x-27))^(1/3).

First few terms can be obtained by Maclaurin's expansion of G.f.

a(n) ~ sqrt((1-s)^3 / (2*s*(3 - 3*s + s^2))) / (2*sqrt(Pi) * n^(3/2) * r^(n-1/2)), where s = 0.31472177038151893868... is the root of the equation 1-2*s-5*s^2+4*s^3 = 0, and r = s*(1-s-2*s^2)/(1-s) = 0.22374229727550306625... - Vaclav Kotesovec, Jan 23 2014

MATHEMATICA

CoefficientList[InverseSeries[Series[x*(1-x-2*x^2)/(1-x), {x, 0, 20}], x], x] (* Vaclav Kotesovec, Jan 22 2014 *)

PROG

(Python)

# a235349. The list a has been calculated (len(a)>=3).

m = len(a)

d = 0

for i in range (1, m+1):

....for j in range (1, m+1):

........if (i+j)%(m+1) ==0 and (i+j) <= (m+1):

............d = d + a[i-1]*a[j-1]

g = 0

for i in range (1, m):

....for j in range (1, m):

........for k in range (1, m):

............if (i+j+k)%(m+1) ==0 and (i+j+k) <= (m+1):

................g = g + a[i-1]*a[j-1]*a[k-1]

y = 2*g + d - a[m-1]

# a235349.

(PARI) Vec(serreverse(x*(1-x-2*x^2)/(1-x)+O(x^66))) \\ Joerg Arndt, Jan 17 2014

CROSSREFS

Cf. A235347.

Sequence in context: A187734 A151353 A151437 * A226157 A264508 A194689

Adjacent sequences:  A235346 A235347 A235348 * A235350 A235351 A235352

KEYWORD

nonn,easy

AUTHOR

Fung Lam, Jan 16 2014

EXTENSIONS

Prepended a(0)=0 to adapt to offset 0, Joerg Arndt, Jan 23 2014

b-file shifted for offset 0, Vaclav Kotesovec, Jan 23 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 09:30 EDT 2022. Contains 353908 sequences. (Running on oeis4.)