A128016 Expansion of (1+x+x^2+x^3)/(1-x^2+x^4).

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

Offset: 0

Author

Paul Barry, Feb 11 2007

Keywords

• easy
• sign

Comments

Periodic{1,1,2,2,1,1,-1,-1,-2,-2,-1,-1}.

Links

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

Crossrefs

Cf. A128017.

Programs

Mathematica

CoefficientList[Series[(1+x+x^2+x^3)/(1-x^2+x^4),{x,0,100}],x] (* or *) LinearRecurrence[{0,1,0,-1},{1,1,2,2},100] (* Harvey P. Dale, Aug 02 2015 *)

Formula

G.f.: (1-x^4)/(1-x-x^2+x^3+x^4-x^5); a(n)=cos(5*pi*n/6)/2+(1-sqrt(3)/2)sin(5*pi*n/6)+cos(pi*n/6)/2+(1+sqrt(3)/2)sin(pi*n/6);