A131193 Period 6: repeat [0, 1, -3, 3, -1, 0].

0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0

Offset: 0

Author

Paul Curtz, Sep 26 2007

Keywords

• sign
• easy

Links

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

Programs

Magma

&cat [[0, 1, -3, 3, -1, 0]^^20]; // Wesley Ivan Hurt, Jun 20 2016

Maple

A131193:=n->[0, 1, -3, 3, -1, 0][(n mod 6)+1]: seq(A131193(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 100, {0, 1, -3, 3, -1, 0}] (* Wesley Ivan Hurt, Jun 20 2016 *)

Formula

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

From Wesley Ivan Hurt, Jun 20 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4.

a(n) = sin(n*Pi/6) * (2*sqrt(3)*cos(n*Pi/6) + 3*sqrt(3)*cos(n*Pi/2) - sin(n*Pi/2) + 8*sin(5*n*Pi/6))/3. (End)