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A132798 Period 6: repeat [0, 2, 1, 0, -2, -1].

%I A132798 #19 Dec 12 2023 08:52:21
%S A132798 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,
%T A132798 -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,
%U A132798 -2,-1,0,2,1,0,-2,-1,0,2,1,0,-2,-1,0,2,1,0,-2,-1
%N A132798 Period 6: repeat [0, 2, 1, 0, -2, -1].
%H A132798 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).
%F A132798 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
%F A132798 a(n) + a(n+1) = A117373(n+4). - _R. J. Mathar_, Jul 22 2009
%F A132798 a(n) = (-n mod 3) * (-1)^floor(n/3) = A080425(n) * (-1)^A002264(n) = A080425(n) * A130151(n). - _Wesley Ivan Hurt_, Jun 20 2014
%F A132798 From _Wesley Ivan Hurt_, Jun 21 2016: (Start)
%F A132798 a(n) + a(n-3) = 0 for n>2.
%F A132798 a(n) = sin(n*Pi/3) * (3*sqrt(3) + 2*sin(2*n*Pi/3))/3. (End)
%p A132798 A132798:=n->(-n mod 3)*(-1)^floor(n/3); seq(A132798(n), n=0..50); # _Wesley Ivan Hurt_, Jun 20 2014
%t A132798 Table[Mod[-n, 3]*(-1)^Floor[n/3], {n, 0, 50}] (* _Wesley Ivan Hurt_, Jun 20 2014 *)
%o A132798 (Magma) [(-n mod 3)*(-1)^Floor(n/3) : n in [0..50]]; // _Wesley Ivan Hurt_, Jun 20 2014
%Y A132798 Cf. A002264, A080425, A117373, A129339, A130151.
%K A132798 sign,easy
%O A132798 0,2
%A A132798 _Paul Curtz_, Nov 21 2007