A124870 - OEIS

%I #12 Sep 18 2024 14:13:30

%S 1,10,25,500,2500,25000,31250,1250000,6250000,62500000,78125000,

%T 3125000000,15625000000,156250000000,195312500000,7812500000000,

%U 39062500000000,390625000000000,488281250000000,19531250000000000

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

%C See A124869 for comments and references.

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

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

%F Conjectures from _Colin Barker_, Jul 16 2019: (Start)

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

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

%F (End)

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

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

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

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

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

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

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

%Y Cf. A124869-A124872.

%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