A132798 Period 6: repeat [0, 2, 1, 0, -2, -1].

0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1

Offset: 0

Author

Paul Curtz, Nov 21 2007

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A002264, A080425, A117373, A129339, A130151.

Programs

Magma

[(-n mod 3)*(-1)^Floor(n/3) : n in [0..50]]; // Wesley Ivan Hurt, Jun 20 2014

Maple

A132798:=n->(-n mod 3)*(-1)^floor(n/3); seq(A132798(n), n=0..50); # Wesley Ivan Hurt, Jun 20 2014

Mathematica

Table[Mod[-n, 3]*(-1)^Floor[n/3], {n, 0, 50}] (* Wesley Ivan Hurt, Jun 20 2014 *)

Formula

G.f.: x*(2+x)/((x+1)*(x^2-x+1)) = (1/3)*(4*x+1)/(x^2-x+1)-(1/3)/(x+1). - R. J. Mathar, Nov 28 2007

a(n) + a(n+1) = A117373(n+4). - R. J. Mathar, Jul 22 2009

a(n) = (-n mod 3) * (-1)^floor(n/3) = A080425(n) * (-1)^A002264(n) = A080425(n) * A130151(n). - Wesley Ivan Hurt, Jun 20 2014

From Wesley Ivan Hurt, Jun 21 2016: (Start)

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

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