login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124869 Numerator of real part of (2*omega)^(-n) where omega = (-1 + i*3)/ 2. 4
1, -1, -2, 13, 7, -79, 11, 307, -527, -481, 779, -3827, -11753, 42641, 4031, -245453, 164833, 897599, -430441, -1044467, 9653287, -14084239, -8545549, 138785587, 32125393, -758178721, 149387939, 2595790093, -5583548873, -1811852719 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalently: numerator of real part of (omega)^(-n) where omega = -1 + i*3. - Harvey P. Dale, Sep 14 2013

LINKS

Table of n, a(n) for n=0..29.

FORMULA

a(n) = numerator( Re(1/(-1 + i*3)^n) ). 1/(-1 + i*3)^n = A124869(n)/ A124870(n) + i*A124871(n)/A124872(n).

G.f.:(10+x)/(10+2*x+x^2) = 1-1/10*x-2/25*x^2+13/500*x^3+7/2500*x^4-79/25000*x^5+... . - Vladeta Jovovic, Oct 08 2007

EXAMPLE

a(0) = 1 = numerator of Re((-1+3*i)^0) = 1/1 + 0*i.

a(1) = -1 = numerator of Re(1/(-1+3*i)) = -1/10 - i*3/10.

a(2) = -2 = numerator of Re((-1+3*i)^(-2)) = -2/25 + i*3/50.

a(3) = 13 = numerator of Re((-1+3*i)^(-3)) = 13/500 + i*9/500.

a(4) = 7 = numerator of Re((-1+3*i)^(-4)) = 7/2500 - i*6/625.

a(5) = -79 = numerator of Re((-1+3*i)^(-5)) = -79/25000 + i*3/25000.

a(6) = 11 = numerator of Re((-1+3*i)^(-6)) = 11/31250 + i*117/125000.

a(7) = 307 = numerator of Re((-1+3*i)^(-7)) = 307/1250000 - i*249/1250000.

a(8) = -527 = numerator of Re((-1+3*i)^(-8)) = -527/6250000 - i*21/390625.

MATHEMATICA

With[{o=-1+3I}, Table[Numerator[Re[o^-n]], {n, 0, 30}]] (* Harvey P. Dale, Sep 14 2013 *)

CROSSREFS

Sequence in context: A128155 A211366 A158088 * A292007 A213825 A244932

Adjacent sequences:  A124866 A124867 A124868 * A124870 A124871 A124872

KEYWORD

easy,frac,sign

AUTHOR

Jonathan Vos Post, Nov 11 2006

EXTENSIONS

Removed square roots from definition and formula. - R. J. Mathar, May 02 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 03:53 EST 2017. Contains 294912 sequences.