A133513 - OEIS

%I #20 Dec 12 2023 08:47:29

%S 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,

%T 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,

%U -1,3,0,1,-3,0,-1,3,0,1,-3,0,-1,3,0,1,-3,0,-1,3

%N Period 6: repeat [0, 1, -3, 0, -1, 3].

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).

%F From _Wesley Ivan Hurt_, Jun 21 2016: (Start)

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

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

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

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

%t PadRight[{}, 100, {0, 1, -3, 0, -1, 3}] (* _Wesley Ivan Hurt_, Jun 21 2016 *)

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

%o (Magma) &cat [[0, 1, -3, 0, -1, 3]^^20]; // _Wesley Ivan Hurt_, Jun 21 2016

%K sign,easy,less

%O 0,3

%A _Paul Curtz_, Nov 30 2007