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

0,3

Links

Table of n, a(n) for n=0..83.

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

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)

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 *)

Prog

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

Crossrefs

Sequence in context: A356326 A261477 A205826 * A350479 A130632 A229158

Adjacent sequences: A131190 A131191 A131192 * A131194 A131195 A131196

Keyword

sign,easy

Author

Paul Curtz, Sep 26 2007

Status

approved