A135695 Period 6: repeat [-1, -1, -2, -2, 3, 3].

-1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1, -1, -2, -2, 3, 3, -1

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. A105899.

Programs

Magma

&cat [[-1, -1, -2, -2, 3, 3]^^20]; // Wesley Ivan Hurt, Jun 22 2016

Maple

A135695 := proc(n) op((n mod 6)+1,[ -1,-1,-2,-2,3,3]) ; end: seq(A135695(n),n=0..150) ; # R. J. Mathar, Feb 07 2009

Mathematica

PadRight[{}, 100, {-1, -1, -2, -2, 3, 3}] (* 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.

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

a(n) = (3*cos(n*Pi/3) - 9*cos(2*n*Pi/3) - 9*sqrt(3)*sin(n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/6. - Wesley Ivan Hurt, Jun 22 2016

Extensions

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