A131533 Period 6: repeat [0, 0, 0, 0, 1, -1].

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

Offset

0,1

Links

Table of n, a(n) for n=0..103.

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

Formula

G.f.: x^4/((x+1)*(x^2+x+1)*(x^2-x+1)). - R. J. Mathar, Nov 14 2007

a(n) = - cos(Pi*n/3)/3 + sin(2*Pi*n/3)/sqrt(3) + (-1)^n/3. - R. J. Mathar, Oct 08 2011

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4. - Wesley Ivan Hurt, Jun 20 2016

Maple

A131533:=n->[0, 0, 0, 0, 1, -1][(n mod 6)+1]: seq(A131533(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 108, {0, 0, 0, 0, 1, -1}] (* Harvey P. Dale, Jan 27 2012 *)

Prog

(PARI) a(n)=[0, 0, 0, 0, 1, -1][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011
(Magma) &cat [[0, 0, 0, 0, 1, -1]^^20]; // Wesley Ivan Hurt, Jun 20 2016

Crossrefs

Sequence in context: A152592 A347412 A275926 * A131532 A353513 A085114

Adjacent sequences: A131530 A131531 A131532 * A131534 A131535 A131536

Keyword

sign,easy,less

Author

Paul Curtz, Aug 26 2007

Extensions

Edited by N. J. A. Sloane, Sep 15 2007

Status

approved