login
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
OFFSET
0,3
FORMULA
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
KEYWORD
sign,easy,less
AUTHOR
Paul Curtz, Nov 30 2007
STATUS
approved