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A132798 Period 6: repeat [0, 2, 1, 0, -2, -1]. 1
0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1, 0, 2, 1, 0, -2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

G.f.: x*(2+x)/((x+1)*(x^2-x+1)) = (1/3)*(4*x+1)/(x^2-x+1)-(1/3)/(x+1). - R. J. Mathar, Nov 28 2007

a(n) = (1/6)*{-(n mod 6)-[(n+1) mod 6]+2*[(n+2) mod 6]+[(n+3) mod 6]+[(n+4) mod 6]-2*[(n+5) mod 6]}. - Paolo P. Lava, Nov 30 2007

a(n) + a(n+1) = A117373(n+4). - R. J. Mathar, Jul 22 2009

a(n) = (-n mod 3) * (-1)^floor(n/3) = A080425(n) * (-1)^A002264(n) = A080425(n) * A130151(n). - Wesley Ivan Hurt, Jun 20 2014

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

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

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

MAPLE

A132798:=n->(-n mod 3)*(-1)^floor(n/3); seq(A132798(n), n=0..50); # Wesley Ivan Hurt, Jun 20 2014

MATHEMATICA

Table[Mod[-n, 3]*(-1)^Floor[n/3], {n, 0, 50}] (* Wesley Ivan Hurt, Jun 20 2014 *)

PROG

(MAGMA) [(-n mod 3)*(-1)^Floor(n/3) : n in [0..50]]; // Wesley Ivan Hurt, Jun 20 2014

CROSSREFS

Cf. A002264, A080425, A117373, A129339, A130151.

Sequence in context: A112201 A112203 A196279 * A080425 A048141 A025664

Adjacent sequences:  A132795 A132796 A132797 * A132799 A132800 A132801

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Nov 21 2007

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)