A133186 Period 4: repeat [1, 2, 1, -4].

1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4

Offset: 0

Author

Paul Curtz, Oct 07 2007

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1).

Crossrefs

Cf. A056594, A109008.

Programs

Magma

&cat [[1, 2, 1, -4]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Maple

seq(op([1, 2, 1, -4]), n=0..40); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

PadRight[{}, 100, {1, 2, 1, -4}] (* Wesley Ivan Hurt, Jul 09 2016 *)

Formula

G.f.: 1/(1+x)+3x/(1+x^2). a(n) = (-1)^n+3*A056594(n-1). [R. J. Mathar, Oct 30 2008]

From Wesley Ivan Hurt, Jul 09 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) = 0 for n>2, a(n) = a(n-4) for n>3.

a(n) = cos(n*Pi) + 3*sin(n*Pi/2). (End)