login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128834 Periodic sequence 0,1,1,0,-1,-1,... 17
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, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Unsigned version in A011655.

LINKS

Table of n, a(n) for n=0..104.

Index entries for sequences related to Chebyshev polynomials.

Index to sequences with linear recurrences with constant coefficients, signature (1,-1).

FORMULA

a(0)=0, a(1)=1, a(n+1) = a(n)-a(n-1) for n>=1.

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

Euler transform of length 6 sequence [ 1, -1, -1, 0, 0, 1]. - Michael Somos, Apr 15 2007

G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= v -u^2 +2*u*v -2*u^2*v. - Michael Somos, Apr 15 2007

G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= v -u^3 +3*u*v -3*u^3*v. - Michael Somos, Apr 15 2007

a(n)=(1/6)*{-(n mod 6)+[(n+2) mod 6]+[(n+3) mod 6]-[(n+5) mod 6]}, with n>=0. - Paolo P. Lava, Jun 11 2007

a(n) = A010892(n-1). - R. J. Mathar, Feb 08 2008

a(n) = A010892(n+5). - Jaume Oliver Lafont, Dec 05 2008

a(n) is multiplicative with a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 3), a(p^e) = (-1)^e if p == 2 (mod 3). - Michael Somos, Apr 15 2007

a(n)=2*sin(n*Pi/3)/sqrt(3). - Jaume Oliver Lafont, Dec 05 2008

From Wolfdieter Lang, Jul 18 2010: (Start)

O.g.f.: x/(1-x+x^2) = x*S(x), with S(x) o.g.f. for Chebyshev S(n,1) = U(n,1/2) = A010892(n).

a(n) = S(n-1,1) = U(n-1,1/2) with S(-1,1)=0. (End)

EXAMPLE

x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 + x^14 - x^16 + ...

MATHEMATICA

PadRight[{}, 120, {0, 1, 1, 0, -1, -1}] (* or *) LinearRecurrence[{1, -1}, {0, 1}, 120] (* Harvey P. Dale, May 08 2014 *)

PROG

(PARI) {a(n)= [0, 1, 1, 0, -1, -1][n%6 +1]}

(Sage)

def A128834():

    x, y = 0, -1

    while true:

        yield -x

        x, y = y, -x + y

a = A128834(); [a.next() for i in range(40)]  # Peter Luschny, Jul 11 2013

CROSSREFS

Sequence in context: A092220 A011655 A102283 * A022928 A000494 A022933

Adjacent sequences:  A128831 A128832 A128833 * A128835 A128836 A128837

KEYWORD

sign,mult,easy

AUTHOR

Philippe Deléham, Apr 13 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 25 18:10 EST 2014. Contains 250000 sequences.