A124872 - OEIS

%I #14 Sep 18 2024 14:13:50

%S 1,10,50,500,625,25000,125000,1250000,390625,62500000,312500000,

%T 3125000000,1953125000,156250000000,781250000000,7812500000000,

%U 1220703125000,390625000000000,1953125000000000,19531250000000000

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

%C See A124871 for comments and references.

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

%e a(0) = 1 = denominator of Im((-1+3*i)^0) = 1/1 + 0*i.

%e a(1) = 10 = denominator of Im(1/(-1+3*i)) = -1/10 - i*3/10.

%e a(2) = 50 = denominator of Im((-1+3*i)^(-2)) = -2/25 + i*3/50.

%e a(3) = 500 = denominator of Im((-1+3*i)^(-3)) = 13/500 + i*9/500.

%e a(4) = 625 = denominator of Im((-1+3*i)^(-4)) = 7/2500 - i*6/625.

%e a(5) = 25000 = denominator of Im((-1+3*i)^(-5)) = -79/25000 + i*3/25000.

%e a(6) = 125000 = denominator of Im((-1+3*i)^(-6)) = 11/31250 + i*117/125000.

%Y Cf. A124869, A124870, A124871 (numerators).

%K easy,frac,nonn

%O 0,2

%A _Jonathan Vos Post_, Nov 11 2006

%E Removed square roots from definition and formula. - _R. J. Mathar_, May 02 2009