A132708 Period 6: repeat [4, 2, 1, -4, -2, -1].

4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1, 4, 2, 1, -4, -2, -1

Offset: 0

Author

Paul Curtz, Nov 16 2007

Keywords

• sign
• easy

Comments

Old definition was: "First differences of 5^n mod 9".

Links

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

Crossrefs

Cf. A070366 (5^n mod 9).

Programs

Magma

&cat [[4,2,1,-4,-2,-1]^^30]; // Wesley Ivan Hurt, Jun 28 2016

Maple

A132708:= n -> [4, 2, 1, -4, -2, -1][(n mod 6)+1]: seq(A132708(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016

Mathematica

PadRight[{}, 120, {4, 2, 1, -4, -2, -1}] (* Harvey P. Dale, Nov 21 2015 *)
Differences[PowerMod[5, Range[0, 90], 9]] (* Alonso del Arte, Jun 04 2016 *)

Formula

G.f.: (x^2 + 2*x + 4)/(x^3 + 1). - Chai Wah Wu, Jun 04 2016

From Wesley Ivan Hurt, Jun 28 2016: (Start)

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

a(n) = a(n-6) for n>5.

a(n) = cos(n*Pi) + 3*cos(n*Pi/3) + sqrt(3)*sin(n*Pi/3). (End)

Extensions

Name changed by Wesley Ivan Hurt, Jun 28 2016