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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

Conjectures from Colin Barker, Jul 16 2019: (Start)

G.f.: (1 - x - 2*x^2 + 13*x^3 - 7*x^4 - 65*x^5 + 39*x^6 + 125*x^7 - 625*x^10) / ((1 - 8*x^2 + 25*x^4)*(1 + 8*x^2 + 25*x^4)).

a(n) = 14*a(n-4) - 625*a(n-8) for n>10.

(End)

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 A333493

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

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)