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A131193 Period 6: repeat [0, 1, -3, 3, -1, 0]. 2
0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0, 0, 1, -3, 3, -1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..83.

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

FORMULA

a(n) = (1/6)*{-[(n+1) mod 6]+4*[(n+2) mod 6]-6*[(n+3) mod 6]+4*[(n+4) mod 6]-[(n+5) mod 6]}. - Paolo P. Lava, Oct 24 2007

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

From Wesley Ivan Hurt, Jun 20 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4.

a(n) = sin(n*Pi/6) * (2*sqrt(3)*cos(n*Pi/6) + 3*sqrt(3)*cos(n*Pi/2) - sin(n*Pi/2) + 8*sin(5*n*Pi/6))/3. (End)

MAPLE

A131193:=n->[0, 1, -3, 3, -1, 0][(n mod 6)+1]: seq(A131193(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

MATHEMATICA

PadRight[{}, 100, {0, 1, -3, 3, -1, 0}] (* Wesley Ivan Hurt, Jun 20 2016 *)

PROG

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

CROSSREFS

Sequence in context: A051343 A261477 A205826 * A130632 A229158 A290454

Adjacent sequences:  A131190 A131191 A131192 * A131194 A131195 A131196

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Sep 26 2007

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)