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!)
A174399 Expansion of (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2). 2
1, -1, 1, -2, 2, -6, 5, -21, 14, -79, 43, -308, 147, -1221, 571, -4868, 2514, -19388, 12144, -76814, 61681, -302007, 318597, -1177274, 1640389, -4553897, 8333655, -17533572, 41583474, -67607944, 203455513, -263678119, 975780382 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

G.f. A(x) satisfies A(x)=1-2x+x*A(x)+x^2*A(x)+x^2*A(x)^2.

Hankel transform is the (essentially) (1,-1) Somos-4 sequence A174400.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2).

D-finite with recurrence: (n+2)*a(n) -(2*n+1)*a(n-1) +5*(1-n)*a(n-2) +5*(2*n-5)*a(n-3) +(n-4)*a(n-4)=0. - R. J. Mathar, Sep 30 2012

Recurrence verified using d.e. (x^5+10*x^4-5*x^3-2*x^2+x) y'' + (5*x^3-5*x^2-3*x+2) y' + 2*x^3-4*x^2+6*x-2 = 0 satisfied by the G.f. - Robert Israel, Jul 21 2019

MAPLE

f:= gfun:-rectoproc({(n+2)*a(n) -(2*n+1)*a(n-1) +5*(1-n)*a(n-2) +5*(2*n-5)*a(n-3) +(n-4)*a(n-4)=0, a(0)=1, a(1)=-1, a(2)=1, a(3)=-2}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Jul 21 2019

MATHEMATICA

CoefficientList[Series[(1-x-x^2-Sqrt[1-2x-5x^2+10x^3+x^4])/(2x^2), {x, 0, 40}], x] (* Harvey P. Dale, Jan 28 2015 *)

PROG

(PARI) x='x+O('x^50); Vec((1-x-x^2-sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2)) \\ G. C. Greubel, Sep 22 2018

(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-x^2-Sqrt(1-2x-5x^2+10x^3+x^4))/(2x^2))); // G. C. Greubel, Sep 22 2018

CROSSREFS

Sequence in context: A054917 A111419 A306768 * A056881 A260322 A286540

Adjacent sequences: A174396 A174397 A174398 * A174400 A174401 A174402

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 18 2010

EXTENSIONS

Corrected and extended by T. D. Noe, Apr 26 2010

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 December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)