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%I #25 Dec 12 2023 09:15:58
%S 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,
%T 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,
%U -1,0,0,1,-1,1,-1,0,0,1,-1,1,-1,0,0,1,-1,1,-1,0
%N Period 6: repeat [0, 1, -1, 1, -1, 0].
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,-1).
%F a(n) = 1/6*cos(1/3*Pi*n)+1/6*3^(1/2)*sin(1/3*Pi*n)+1/2*cos(2/3*Pi*n)+1/6*3^(1/2)*sin(2/3*Pi*n)+2/3*(-1)^(1+n). - _R. J. Mathar_, Nov 15 2007
%F G.f.: x*(x^2+1) / ((x+1)*(x^2-x+1)*(x^2+x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%F a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4. - _Wesley Ivan Hurt_, Jun 20 2016
%p A131720:=n->[0, 1, -1, 1, -1, 0][(n mod 6)+1]: seq(A131720(n), n=0..100); # _Wesley Ivan Hurt_, Jun 20 2016
%t PadRight[{}, 100, {0,1,-1,1,-1,0}] (* _Harvey P. Dale_, Aug 20 2015 *)
%o (PARI) a(n)=[0,1,-1,1,-1,0][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat [[0, 1, -1, 1, -1, 0]^^20]; // _Wesley Ivan Hurt_, Jun 20 2016
%K sign,easy,less
%O 0,1
%A _Paul Curtz_, Sep 15 2007
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