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%I #13 Dec 12 2023 08:13:56
%S 4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,
%T 4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,3,4,4,0,4,
%U 3,4
%N Periodic sequence [4,0,4,3,4] of period 5
%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(2) = a(4) = 4, a(1) = 0 and a(3) = 3
%F a(n) = 3+(1/2-3/10*5^(1/2))*cos(2*n*Pi/5)+(-1/10*(4*(5+5^(1/2))^(1/2)-(5-5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(3/10*5^(1/2)+1/2)*cos(4*n*Pi/5)+(-1/10*((5+5^(1/2))^(1/2)+4*(5-5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5)
%F o.g.f f(z) = (4+4*z^2+3*z^3+4*z^4)/(1-z^5)
%t PadRight[{},100,{4,0,4,3,4}] (* _Harvey P. Dale_, Jun 08 2014 *)
%Y A026042
%K easy,nonn
%O 0,1
%A _Richard Choulet_, Dec 14 2008
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