A132419 Period 6: repeat [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, -1

Offset: 0

Author

Paul Curtz, Nov 13 2007

Keywords

• sign
• easy
• less

Links

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

Crossrefs

Cf. A061347.

Programs

Magma

&cat [[1, 1, -2, -1, -1, 2]^^20]; // Wesley Ivan Hurt, Jun 21 2016

Maple

A132419:=n->[1, 1, -2, -1, -1, 2][(n mod 6)+1]: seq(A132419(n), n=0..100); # Wesley Ivan Hurt, Jun 21 2016

Mathematica

PadRight[{}, 100, {1, 1, -2, -1, -1, 2}] (* Wesley Ivan Hurt, Jun 21 2016 *)

PARI

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

Formula

a(n) = A061347(n+1) * (-1)^floor(n/3).

From Wesley Ivan Hurt, Jun 21 2016: (Start)

G.f.: (1+x-2*x^2)/(1+x^3).

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

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

Extensions

Comment changed to formula by Wesley Ivan Hurt, Jun 21 2016