A131533 Period 6: repeat [0, 0, 0, 0, 1, -1].

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

Offset: 0

Author

Paul Curtz, Aug 26 2007

Keywords

• sign
• easy
• less

Links

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

Programs

Magma

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

Maple

A131533:=n->[0, 0, 0, 0, 1, -1][(n mod 6)+1]: seq(A131533(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 108, {0,0,0,0,1,-1}] (* Harvey P. Dale, Jan 27 2012 *)

PARI

a(n)=[0,0,0,0,1,-1][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

G.f.: x^4/((x+1)*(x^2+x+1)*(x^2-x+1)). - R. J. Mathar, Nov 14 2007

a(n) = - cos(Pi*n/3)/3 + sin(2*Pi*n/3)/sqrt(3) + (-1)^n/3. - R. J. Mathar, Oct 08 2011

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4. - Wesley Ivan Hurt, Jun 20 2016

Extensions

Edited by N. J. A. Sloane, Sep 15 2007