A124871 Numerator of imaginary part of (3*i - 1)^(-n).

0, -3, 3, 9, -6, 3, 117, -249, -21, 1917, -237, -9111, 1287, 24963, -76443, 28071, 11067, -848643, -922077, 6087369, -184623, -27482877, 34867797, 67678791, -15126111, 145641597, 1064447283, -2857102551, -308141733, 19215780483, -6890111163

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..2859

Formula

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

Example

a(0) = 0 = numerator of Im((-1+3*i)^0) = 1/1 + 0*i.
a(1) = -3 = numerator of Im(1/(-1+3*i)) = -1/10 - i*3/10.
a(2) = 3 = numerator of Im((-1+3*i)^(-2)) = -2/25 + i*3/50.
a(3) = 9 = numerator of Im((-1+3*i)^(-3)) = 13/500 + i*9/500.
a(4) = -6 = numerator of Im((-1+3*i)^(-4)) = 7/2500 - i*6/625.
a(5) = 3 = numerator of Im((-1+3*i)^(-5)) = -79/25000 + i*3/25000.
a(6) = 117 = numerator of Im((-1+3*i)^(-6)) = 11/31250 + i*117/125000.
a(7) = -249 = numerator of Im((-1+3*i)^(-7)) = 307/1250000 - i*249/1250000.
a(8) = -21 = numerator of Im((-1+3*i)^(-8)) = -527/6250000 - i*21/390625.

Maple

B:= gfun:-rectoproc({-10*b(x + 2) - 2*b(x + 1) - b(x), b(0) = 0, b(1) = -3/10}, b(x), remember):
map(numer, [seq(B(n), n=0..50)]); # Robert Israel, Feb 02 2020

Crossrefs

Cf. A124869, A124870, A124872.

Sequence in context: A294178 A062131 A199663 * A197414 A247571 A292885

Adjacent sequences: A124868 A124869 A124870 * A124872 A124873 A124874

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