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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184120 Expansion of (1/(1+4x+2x^2))*c(x/(1+4x+2x^2)), c(x) the g.f. of A000108. 2
1, -3, 8, -23, 70, -218, 688, -2195, 7062, -22866, 74416, -243206, 797660, -2624004, 8654304, -28607171, 94748774, -314361682, 1044625200, -3476135186, 11581870900, -38632753228, 128998096032, -431144781486, 1442252806012 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is the (4,-3) Somos-4 sequence A184121.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (sqrt(2*x^2+4*x+1)-sqrt(2*x^2+1))/(2*x*sqrt(2*x^2+4*x+1)).

G.f.: 1/(1+4x+2x^2-x/(1-x/(1+4x+2x^2-x/(1-x/(1+4x+2x^2-x/(1-x/(1-... (continued fraction).

Conjecture: (n+1)*a(n) +2*(2n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(2n-5)*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 17 2011

G.f.: 1/(2*x) - G(0)/(2*x), where G(k)= 1 - 4*x*(4*k+1)/( (1+2*x^2)*(4*k+2) - x*(1+2*x^2)*(4*k+2)*(4*k+3)/(x*(4*k+3) - (1+2*x^2)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 26 2013

a(n) ~ (-1)^n * (2+sqrt(2))^n / (sqrt(3*sqrt(2)-4) * sqrt(Pi*n)). - Vaclav Kotesovec, Feb 04 2014

MATHEMATICA

CoefficientList[Series[(Sqrt[2x^2+4x+1]-Sqrt[2x^2+1])/(2x Sqrt[2x^2+4x+1]), {x, 0, 30}], x] (* Harvey P. Dale, Mar 09 2012 *)

PROG

(PARI) x='x+O('x^30); Vec((sqrt(2*x^2+4*x+1)-sqrt(2*x^2+1))/( 2*x*sqrt(2*x^2+4*x+1))) \\ G. C. Greubel, Aug 14 2018

(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((Sqrt(2*x^2+4*x+1)-Sqrt(2*x^2+1))/( 2*x*Sqrt(2*x^2+4*x+1)))); // G. C. Greubel, Aug 14 2018

CROSSREFS

Sequence in context: A193418 A005960 A273716 * A215512 A061557 A000782

Adjacent sequences: A184117 A184118 A184119 * A184121 A184122 A184123

KEYWORD

sign,easy

AUTHOR

Paul Barry, Jan 09 2011

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 November 27 06:50 EST 2022. Contains 358362 sequences. (Running on oeis4.)