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%I #49 Dec 12 2023 09:26:14
%S 0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,
%T 0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,
%U 0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0
%N Period 4: repeat [0, 1, 0, 2].
%C Least positive integer k such that n^k == 1 (mod 4), or 0 if GCD(n,4) > 1. - _Bruno Berselli_, Mar 22 2016
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F G.f.: x*(1+2*x^2)/ ((1-x)*(x+1)*(x^2+1)). - _R. J. Mathar_, Nov 15 2007
%F a(n) = 3/4-1/2*sin(1/2*Pi*n)+3/4*(-1)^(1+n). - _R. J. Mathar_, Nov 15 2007
%F a(n) = Fibonacci(2*n) mod 3. - _Gary Detlefs_ Feb 13 2011
%F a(n) == A006368(n) (mod 3). - _Philippe Deléham_, Oct 24 2011
%F a(n) = a(n-4) for n>3. - _Wesley Ivan Hurt_, Jul 09 2016
%p seq(op([0, 1, 0, 2]), n=0..50); # _Wesley Ivan Hurt_, Jul 09 2016
%t PadRight[{}, 106, {0, 1, 0, 2}] (* _Harvey P. Dale_, Apr 06 2012 *)
%t CoefficientList[Series[x (1 + 2 x^2)/((1 - x) (x + 1) (x^2 + 1)), {x, 0, 120}], x] (* _Michael De Vlieger_, Jul 09 2016 *)
%o (Magma) &cat [[0, 1, 0, 2]^^30]; // _Bruno Berselli_, Mar 22 2016
%o (PARI) x='x+O('x^200); concat(0, Vec(-x*(1+2*x^2)/((x-1)*(x+1)*(x^2+1)))) \\ _Altug Alkan_, Mar 22 2016
%o (PARI) a(n)=n%2*(n%4+1)/2 \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Python)
%o def A131743(n): return (0,1,0,2)[n&3] # _Chai Wah Wu_, Jul 29 2023
%Y Cf. A006368.
%K nonn,easy
%O 0,4
%A _Paul Curtz_, Sep 20 2007
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