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%I #19 Apr 07 2024 17:42:29
%S 1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,
%T 0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,
%U 0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0,1,0,4,0,0
%N Periodic sequence [1,0,4,0,0] 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) = 1, a(2) = a(3) = a(4) = 0 and a(2) = 4.
%F O.g.f: (1+4z^2)/(1-z^5).
%F a(n) = 1-2/5*5^(1/2)*cos(2*n*Pi/5)+2/5*2^(1/2)*(5-5^(1/2))^(1/2)*sin(2*n*Pi/5) + 2/5*5^(1/2)*cos(4*n*Pi/5)-2/5*2^(1/2)*(5+5^(1/2))^(1/2)*sin(4*n*Pi/5).
%Y Cf. A026048.
%K easy,nonn
%O 0,3
%A _Richard Choulet_, Dec 14 2008
%E More terms from _Philippe Deléham_, Dec 29 2008
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