A131736 Period 6: repeat [0, 0, 1, -1, -1, 1].

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

Offset: 0

Author

Paul Curtz, Sep 19 2007

Keywords

• sign
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1).

Crossrefs

Cf. A022003, A131532.

Programs

Mathematica

PadRight[{}, 100, {0, 0, 1, -1, -1, 1}] (* Wesley Ivan Hurt, Jan 15 2017 *)

Formula

From Matthew House, Jan 15 2017: (Start)

G.f.: x^2*(1-x)/(1+x^2+x^4).

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

a(n) = sin(n*Pi/6) * (3*sin(n*Pi/2) - 2*sqrt(3)*cos(n*Pi/6) - 3*sqrt(3)*cos(n*Pi/2)) / 3. - Wesley Ivan Hurt, Apr 26 2020

From Nicolas Bělohoubek, Jun 05 2025: (Start)

a(n) = A022003(n) - A131532(n+1).

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

Extensions

Title edited by Matthew House, Jan 15 2017