A102560 Expansion of (1-x^3)/(1-x^4).

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

Offset: 0

Author

Paul Barry, Jan 14 2005

Keywords

• easy
• sign

Comments

Period 4: repeat [1, 0, 0, -1].

Links

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

Programs

Magma

&cat [[1, 0, 0, -1]^^30]; // Wesley Ivan Hurt, Jul 06 2016

Maple

seq(op([1, 0, 0, -1]), n=0..50); # Wesley Ivan Hurt, Jul 06 2016

Mathematica

CoefficientList[ Series[(1 - x^3)/(1 - x^4), {x, 0, 105}], x] (* Robert G. Wilson v, Jan 15 2005 *)

PARI

x='x+O('x^50); Vec((1 - x^3)/(1 - x^4)) \\ G. C. Greubel, Jun 02 2017

Formula

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

a(n) = (-1)^floor(n/2)/2+(-1)^n/2.

a(n) = cos(Pi*n/2)/2 + sin(Pi*n/2)/2 + cos(Pi*n)/2.

a(n) = -a(n-1)-a(n-2)-a(n-3) for n>2 with a(0)=1, a(1)=a(2)=0. - Jaume Oliver Lafont, Dec 05 2008