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%I #26 Dec 12 2023 08:54:38
%S 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,
%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,-2,1,1,2,-1,-1,-2
%N Period 6: repeat [1, 1, 2, -1, -1, -2].
%C Nonsimple continued fraction expansion of 1+1/sqrt(3) = 1 + A020760. - _R. J. Mathar_, Mar 08 2012
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).
%F a(n) = cos(Pi*n/3)/3+sqrt(3)*sin(Pi*n/3)+2*(-1)^n/3. - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, Jun 19 2016: (Start)
%F G.f.: (1+x+2*x^2)/(1+x^3).
%F a(n) + a(n-3) = 0 for n>2. (End)
%p A132367:=n->[1, 1, 2, -1, -1, -2][(n mod 6)+1]: seq(A132367(n), n=0..100); # _Wesley Ivan Hurt_, Jun 19 2016
%t PadRight[{}, 120, {1,1,2,-1,-1,-2}] (* _Harvey P. Dale_, Jul 28 2012 *)
%o (PARI) a(n)=[1,1,2,-1,-1,-2][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat[[1, 1, 2, -1, -1, -2]^^20]; // _Wesley Ivan Hurt_, Jun 19 2016
%Y Cf. A020760, A061347, A100051, A100063, A122876.
%K sign,easy,less
%O 0,3
%A _Paul Curtz_, Nov 09 2007
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