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%I #26 Dec 12 2023 09:18:26
%S 1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,
%T -1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,
%U 1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1,1,-2,1,-1,2,-1
%N Period 6: repeat [1, -2, 1, -1, 2, -1].
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).
%F G.f.: (x-1)^2/(x+1)/(x^2-x+1). - _R. J. Mathar_, Nov 14 2007
%F a(n) = (-1)^n * A131534(n). - _R. J. Mathar_, Apr 02 2011
%F a(n) = -cos(Pi*n/3)/3 -sin(Pi*n/3)/sqrt(3) +4*(-1)^n/3. - _R. J. Mathar_, Oct 08 2011
%F a(n) + a(n-3) = 0 for n>2. - _Wesley Ivan Hurt_, Jun 19 2016
%p A131556:=n->[1, -2, 1, -1, 2, -1][(n mod 6)+1]: seq(A131556(n), n=0..100); # _Wesley Ivan Hurt_, Jun 19 2016
%t PadRight[{}, 100, {1, -2, 1, -1, 2, -1}] (* _Wesley Ivan Hurt_, Jun 19 2016 *)
%o (PARI) a(n)=[1,-2,1,-1,2,-1][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat[[1, -2, 1, -1, 2, -1]^^20]; // _Wesley Ivan Hurt_, Jun 19 2016
%Y Cf. A131534.
%K sign,easy,less
%O 0,2
%A _Paul Curtz_, Aug 27 2007
%E Edited by _N. J. A. Sloane_, Sep 15 2007
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