A131556 Period 6: repeat [1, -2, 1, -1, 2, -1].

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

Offset: 0

Author

Paul Curtz, Aug 27 2007

Keywords

• sign
• easy
• less

Links

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

Crossrefs

Cf. A131534.

Programs

Magma

&cat[[1, -2, 1, -1, 2, -1]^^20]; // Wesley Ivan Hurt, Jun 19 2016

Maple

A131556:=n->[1, -2, 1, -1, 2, -1][(n mod 6)+1]: seq(A131556(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016

Mathematica

PadRight[{}, 100, {1, -2, 1, -1, 2, -1}] (* Wesley Ivan Hurt, Jun 19 2016 *)

PARI

a(n)=[1,-2,1,-1,2,-1][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

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

a(n) = (-1)^n * A131534(n). - R. J. Mathar, Apr 02 2011

a(n) = -cos(Pi*n/3)/3 -sin(Pi*n/3)/sqrt(3) +4*(-1)^n/3. - R. J. Mathar, Oct 08 2011

a(n) + a(n-3) = 0 for n>2. - Wesley Ivan Hurt, Jun 19 2016

Extensions

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