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A110568 Period 6: repeat [1, 0, 2, 2, 0, 1].

%I A110568 #31 Dec 14 2023 05:18:12
%S A110568 1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,
%T A110568 0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,
%U A110568 2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2,2,0,1,1,0,2
%N A110568 Period 6: repeat [1, 0, 2, 2, 0, 1].
%C A110568 Permutation of {0, 1, 2}, followed by its reversal, repeated.
%H A110568 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).
%F A110568 a(n) = A078008(n) mod 3.
%F A110568 G.f.: (1-x+3*x^2-x^3+x^4) / (1-x+x^2-x^3+x^4-x^5).
%F A110568 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.
%F A110568 a(n) = 1 + cos(2*Pi*n/3)/2 - sqrt(3)*sin(2*Pi*n/3)/2 - cos(Pi*n/3)/2 + sqrt(3)*sin(Pi*n/3)/6.
%F A110568 a(n) = a(n-6) for n > 5. - _Wesley Ivan Hurt_, Jun 28 2016
%F A110568 a(n) = ((n-1)*(-1)^(n-1) mod 3). - _Wesley Ivan Hurt_, Jan 07 2021
%p A110568 A110568:=n->[1, 0, 2, 2, 0, 1][(n mod 6)+1]: seq(A110568(n), n=0..100); # _Wesley Ivan Hurt_, Jun 28 2016
%t A110568 Mod[#,3]&/@CoefficientList[Series[(1-x)/(1-x-2x^2),{x,0,100}],x] (* _Harvey P. Dale_, Mar 30 2011 *)
%t A110568 PadRight[{}, 100, {1, 0, 2, 2, 0, 1}] (* _Wesley Ivan Hurt_, Jun 28 2016 *)
%t A110568 LinearRecurrence[{1,-1,1,-1,1},{1,0,2,2,0},100] (* _Harvey P. Dale_, Apr 03 2019 *)
%o A110568 (Magma) &cat [[1, 0, 2, 2, 0, 1]^^30]; // _Wesley Ivan Hurt_, Jun 28 2016
%o A110568 (PARI) x='x+O('x^50); Vec((1-x+3*x^2-x^3+x^4)/(1-x+x^2-x^3+x^4-x^5)) \\ _G. C. Greubel_, Aug 31 2017
%Y A110568 Cf. A078008, A088689, A105198, A110549, A110550, A110551, A110569.
%K A110568 easy,nonn
%O A110568 0,3
%A A110568 _Paul Barry_, Jul 27 2005
%E A110568 Name changed by _Wesley Ivan Hurt_, Jun 28 2016