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%I #24 Dec 12 2023 08:06:50
%S 0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,
%T 1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,
%U 0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1
%N Period 5: repeat [0, 3, 1, 0, 1].
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F a(n+5) = a(n) with a(0) = a(3) = 0, a(1) = 3 and a(2) = a(4) = 1.
%F O.g.f: ((3*z+z^2+z^4)/(1-z^5)).
%F a(n) = 1 + (-1/2 + (3/10)*sqrt(5))*cos(2*n*Pi/5) + ((1/5)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/10)*sqrt(2)*sqrt(5 - sqrt(5)))*sin(2*n*Pi/5) + (-1/2 - (3/10)*sqrt(5))*cos(4*n*Pi/5) + (-(1/10)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/5)*sqrt(2)*sqrt(5-sqrt(5)))*sin(4*n*Pi/5).
%F a(n) = (n^3 + 2*n^2) mod 5. - _Gary Detlefs_, Mar 20 2010
%p seq((n^3+2*n^2)mod 5,n=0..50); # _Gary Detlefs_, Mar 20 2010
%t PadRight[{},120,{0,3,1,0,1}] (* _Harvey P. Dale_, Oct 04 2016 *)
%Y Cf. A026053, A026068.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Dec 14 2008