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

%I #20 Dec 12 2023 09:07:52

%S 0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,-1,

%T 1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,1,-1,

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

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

%H Matthew House, <a href="/A131736/b131736.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,-1).

%F From _Matthew House_, Jan 15 2017: (Start)

%F G.f.: x^2*(1-x)/(1+x^2+x^4).

%F a(n) = -a(n-2) - a(n-4) for n > 3. (End)

%F a(n) = sin(n*Pi/6) * (3*sin(n*Pi/2) - 2*sqrt(3)*cos(n*Pi/6) - 3*sqrt(3)*cos(n*Pi/2)) / 3. - _Wesley Ivan Hurt_, Apr 26 2020

%t PadRight[{}, 100, {0, 0, 1, -1, -1, 1}] (* _Wesley Ivan Hurt_, Jan 15 2017 *)

%K sign,easy

%O 0,1

%A _Paul Curtz_, Sep 19 2007

%E Title edited by _Matthew House_, Jan 15 2017