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A133513 Period 6: repeat [0, 1, -3, 0, -1, 3]. 2
0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3, 0, 1, -3, 0, -1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..77.

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

FORMULA

a(n) = (1/6)*{3*(n mod 6)-4*[(n+1) mod 6]+[(n+2) mod 6]-3*[(n+3) mod 6]+4*[(n+4) mod 6]-[(n+5) mod 6]}. - Paolo P. Lava, Dec 06 2007

From Wesley Ivan Hurt, Jun 21 2016: (Start)

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

a(n) + a(n-3) = 0 for n>2.

a(n) = 2 * sin(n*Pi/3) * (4*sin(2*n*Pi/3) - sqrt(3))/3. (End)

MAPLE

A133513:=n->[0, 1, -3, 0, -1, 3][(n mod 6)+1]: seq(A133513(n), n=0..100); # Wesley Ivan Hurt, Jun 21 2016

MATHEMATICA

PadRight[{}, 100, {0, 1, -3, 0, -1, 3}] (* Wesley Ivan Hurt, Jun 21 2016 *)

PROG

(PARI) a(n)=[0, 1, -3, 0, -1, 3][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

(MAGMA) &cat [[0, 1, -3, 0, -1, 3]^^20]; // Wesley Ivan Hurt, Jun 21 2016

CROSSREFS

Sequence in context: A071818 A014513 A144388 * A101000 A035653 A126595

Adjacent sequences:  A133510 A133511 A133512 * A133514 A133515 A133516

KEYWORD

sign,easy,less

AUTHOR

Paul Curtz, Nov 30 2007

STATUS

approved

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Last modified April 18 12:34 EDT 2019. Contains 322209 sequences. (Running on oeis4.)