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A216178 Period 4: repeat [4, 1, 0, -3].

%I A216178 #25 Sep 08 2022 08:46:03
%S A216178 4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,
%T A216178 -3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,
%U A216178 1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3,4,1,0,-3
%N A216178 Period 4: repeat [4, 1, 0, -3].
%H A216178 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A216178 a(n) = (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4).
%F A216178 a(n) = A168361(n+1) + A084100(n+4).
%F A216178 G.f.: (4+x-3*x^3) / ((1-x)*(1+x)*(1+x^2)). - _R. J. Mathar_, Mar 10 2013
%F A216178 a(n+4) = a(n). - _Alexander R. Povolotsky_, Mar 15 2013
%F A216178 From _Wesley Ivan Hurt_, Jul 09 2016: (Start)
%F A216178 a(n) = 1/2+3*I^(2*n)/2+(1+I)*I^(-n)+(1-I)*I^n.
%F A216178 a(n) = (1+3*cos(n*Pi)+4*cos(n*Pi/2)+4*sin(n*Pi/2)+3*I*sin(n*Pi))/2. (End)
%p A216178 seq(op([4, 1, 0, -3]), n=0..40); # _Wesley Ivan Hurt_, Jul 09 2016
%t A216178 PadRight[{},100,{4,1,0,-3}] (* or *) LinearRecurrence[{0,0,0,1},{4,1,0,-3},100] (* _Harvey P. Dale_, Nov 28 2014 *)
%o A216178 (Magma) for n in [0 .. 50] do (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4); end for;
%o A216178 (Magma) &cat [[4, 1, 0, -3]^^30]; // _Wesley Ivan Hurt_, Jul 09 2016
%o A216178 (PARI) a(n)=[4, 1, 0, -3][n%4+1] \\ _Charles R Greathouse IV_, Jul 17 2016
%Y A216178 Cf. A084100, A168361, A214864.
%K A216178 sign,easy
%O A216178 0,1
%A A216178 _Brad Clardy_, Mar 10 2013