A124870 Denominator of real part of (3*i - 1)^(-n).

1, 10, 25, 500, 2500, 25000, 31250, 1250000, 6250000, 62500000, 78125000, 3125000000, 15625000000, 156250000000, 195312500000, 7812500000000, 39062500000000, 390625000000000, 488281250000000, 19531250000000000

Offset

0,2

Comments

See A124869 for comments and references.

Links

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

Formula

a(n) = denominator(Re(1/(-1 + i*3)^n) ).

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

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

G.f.: (1 + 10*x + 25*x^2 + 500*x^3 - 31250*x^6) / ((1 - 50*x^2)*(1 + 50*x^2)).

a(n) = 2500*a(n-4) for n>6.

(End)

Example

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

Crossrefs

Cf. A124869-A124872.

Sequence in context: A220039 A219377 A156183 * A078257 A372520 A059198

Adjacent sequences: A124867 A124868 A124869 * A124871 A124872 A124873

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Nov 11 2006

Extensions

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

Status

approved