A238187 Gaussian norm of 1+(1+i)^n.

4, 5, 5, 5, 9, 25, 65, 145, 289, 545, 1025, 1985, 3969, 8065, 16385, 33025, 66049, 131585, 262145, 523265, 1046529, 2095105, 4194305, 8392705, 16785409, 33562625, 67108865, 134201345, 268402689, 536838145, 1073741825, 2147549185, 4295098369, 8590065665

Offset: 0

Author

Cristóbal Camarero, Feb 19 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Programs

Magma

[Floor(2^n+(1+Sqrt(-1))^n+(1-Sqrt(-1))^n+1): n in [0..40]]; // Vincenzo Librandi, Feb 21 2014

Maple

seq(GInorm(1+(1+I)**n),n=0..33);

Mathematica

Table[Norm[{1 + (1 + I)^n}]^2, {n, 0, 40}] (* Bruno Berselli, Feb 20 2014 *)
CoefficientList[Series[-(10 x^3 - 20 x^2 + 15 x - 4)/((x - 1) (2 x - 1) (2 x^2 - 2 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 21 2014 *)

PARI

a(n) = norml2(1+(1+I)^n); \\ Michel Marcus, Feb 19 2014

Formula

G.f.: -(10*x^3-20*x^2+15*x-4)/((x-1)*(2*x-1)*(2*x^2-2*x+1)). [Joerg Arndt, Feb 20 2014]

a(n) = 2^n + (1+i)^n + (1-i)^n + 1. [Bruno Berselli, Feb 20 2014]