A124872 Denominator of imaginary part of (3*i - 1)^(-n).

1, 10, 50, 500, 625, 25000, 125000, 1250000, 390625, 62500000, 312500000, 3125000000, 1953125000, 156250000000, 781250000000, 7812500000000, 1220703125000, 390625000000000, 1953125000000000, 19531250000000000

Offset

0,2

Comments

See A124871 for comments and references.

Links

Table of n, a(n) for n=0..19.

Formula

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

Example

a(0) = 1 = denominator of Im((-1+3*i)^0) = 1/1 + 0*i.
a(1) = 10 = denominator of Im(1/(-1+3*i)) = -1/10 - i*3/10.
a(2) = 50 = denominator of Im((-1+3*i)^(-2)) = -2/25 + i*3/50.
a(3) = 500 = denominator of Im((-1+3*i)^(-3)) = 13/500 + i*9/500.
a(4) = 625 = denominator of Im((-1+3*i)^(-4)) = 7/2500 - i*6/625.
a(5) = 25000 = denominator of Im((-1+3*i)^(-5)) = -79/25000 + i*3/25000.
a(6) = 125000 = denominator of Im((-1+3*i)^(-6)) = 11/31250 + i*117/125000.

Crossrefs

Cf. A124869, A124870, A124871 (numerators).

Sequence in context: A154410 A060156 A000450 * A240534 A223161 A216156

Adjacent sequences: A124869 A124870 A124871 * A124873 A124874 A124875

Keyword

easy,frac,nonn,changed

Author

Jonathan Vos Post, Nov 11 2006

Extensions

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

Status

approved