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A102560 Expansion of (1-x^3)/(1-x^4). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..108.

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

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) = (1/4)*{-2*(n mod 4)+[(n+1) mod 4]+[(n+3) mod 4]}. - Paolo P. Lava, Oct 23 2007

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

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 *)

PROG

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

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

CROSSREFS

Sequence in context: A190198 A071004 A188083 * A190669 A285258 A068428

Adjacent sequences:  A102557 A102558 A102559 * A102561 A102562 A102563

KEYWORD

easy,sign

AUTHOR

Paul Barry, Jan 14 2005

STATUS

approved

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Last modified July 25 19:28 EDT 2021. Contains 346291 sequences. (Running on oeis4.)