|
%I #16 Dec 12 2023 08:14:38
%S 0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,
%T 0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,0,0,0,2,3,
%U 0,0
%N Period 5: repeat [0, 2, 3, 0, 0].
%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) = a(4) = 0, a(1) = 2 and a(2) = 3.
%F O.g.f f(z) = (2*z+3*z^2)/(1-z^5).
%F a(n) = 1+(-1/2-1/10*5^(1/2))*cos(2*n*Pi/5)+(1/10*(3*(5-5^(1/2))^(1/2)+2*(5+5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(1/10*5^(1/2)-1/2)*cos(4*n*Pi/5)+(1/10*(2*(5-5^(1/2))^(1/2)-3*(5+5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5).
%F a(n) = (5 + 4*cos(2*(n-1)*Pi/5) + 4*cos(4*(n-1)*Pi/5) + 6*cos(2*(n+3)*Pi/5) + 6*cos(4*(n+3)*Pi/5))/5. - _Wesley Ivan Hurt_, Jun 25 2022
%t PadRight[{},100,{0,2,3,0,0}] (* _Harvey P. Dale_, Aug 09 2021 *)
%Y Cf. A026045.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Dec 14 2008
|
