A135694 Period 6: repeat [1, -1, -1, -1, 0, 2].

1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2, 1, -1, -1, -1, 0, 2

Offset: 0

Author

Paul Curtz, Feb 24 2008

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A000079, A049347, A119910, A135575.

Programs

Magma

&cat [[1, -1, -1, -1, 0, 2]^^20]; // Wesley Ivan Hurt, Jun 22 2016

Maple

A135694 := proc(n) op((n mod 6)+1,[1,-1,-1,-1,0,2]) ; end: seq(A135694(n), n=0..150) ; # R. J. Mathar, Feb 07 2009

Mathematica

PadRight[{}, 100, {1, -1, -1, -1, 0, 2}] (* Wesley Ivan Hurt, Jun 22 2016 *)

Formula

From R. J. Mathar, Mar 31 2008: (Start)

a(n) = a(n-6) for n>5. a(n) = -a(n-2) - a(n-4) for n>3.

a(n) = (A119910(n+3) - A049347(n+1))/2 for n>0.

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

a(n) = (3*cos(n*Pi/3) - 8*sqrt(3)*cos(n*Pi/6)^3*sin(n*Pi/6))/3. - Wesley Ivan Hurt, Jun 22 2016

Extensions

More periods from R. J. Mathar, Feb 07 2009