A131720 Period 6: repeat [0, 1, -1, 1, -1, 0].

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

Offset: 0

Author

Paul Curtz, Sep 15 2007

Keywords

• sign
• easy
• less

Links

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

Programs

Magma

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

Maple

A131720:=n->[0, 1, -1, 1, -1, 0][(n mod 6)+1]: seq(A131720(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 100, {0,1,-1,1,-1,0}] (* Harvey P. Dale, Aug 20 2015 *)

PARI

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

Formula

a(n) = 1/6*cos(1/3*Pi*n)+1/6*3^(1/2)*sin(1/3*Pi*n)+1/2*cos(2/3*Pi*n)+1/6*3^(1/2)*sin(2/3*Pi*n)+2/3*(-1)^(1+n). - R. J. Mathar, Nov 15 2007

G.f.: x*(x^2+1) / ((x+1)*(x^2-x+1)*(x^2+x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

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