A174784 Expansion of x*(1-x+x^3+x^4)/(1+x^6) (Period 12).

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

Offset: 0

Author

Paul Barry, Mar 29 2010

Keywords

• easy
• sign

Comments

Hankel transform of A174783 is -a(n).

Links

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

Programs

Mathematica

LinearRecurrence[{0,0,0,0,0,-1},{0,1,-1,0,1,1},100] (* or *) PadRight[ {},120,{0,1,-1,0,1,1,0,-1,1,0,-1,-1}] (* Harvey P. Dale, Feb 25 2017 *)

Formula

a(n) = -cos(5*Pi*n/6)/3 + sin(5*Pi*n/6)/3 - cos(Pi*n/6)/3 + sin(Pi*n/6)/3 + 2*cos(Pi*n/2)/3 + 2*sin(Pi*n/2)/3.

G.f.: x*(1-x+x^3+x^4) / ( (1+x^2)*(x^4-x^2+1) ). - R. J. Mathar, Feb 10 2015