A131714 Period 6: repeat [1, -2, 2, -1, 2, -2].

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

Offset: 0

Author

Paul Curtz, Sep 14 2007

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,-1).

Crossrefs

Cf. A130196, A131556.

Programs

Magma

&cat[[1, -2, 2, -1, 2, -2]^^20]; // Wesley Ivan Hurt, Jun 19 2016

Maple

A131714:=n->[1, -2, 2, -1, 2, -2][(n mod 6)+1]: seq(A131714(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016

Mathematica

PadRight[{}, 200, {1, -2, 2, -1, 2, -2}] (* Wesley Ivan Hurt, Jun 19 2016 *)

Formula

G.f.: (1-2*x+2*x^2)/(x+1)/(x^2-x+1). - R. J. Mathar, Nov 14 2007

From Wesley Ivan Hurt, Jun 19 2016: (Start)

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

a(n) = (5*cos(n*Pi)-2*cos(n*Pi/3))/3. (End)