A120323 - OEIS

%I #11 Sep 14 2024 02:27:51

%S 0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,

%T 1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,1,0,1,3,0,3,

%U 1,0,1,3,0,3,1,0,1,3,0

%N Periodic sequence 0, 3, 1, 0, 1, 3.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F a(n) = (4/3)*(sin(n*Pi/6)+sin(n*Pi/2))^2.

%e n=0 (4/3)*(sin(0)+sin(0))^2 = 0.

%e n=1 (4/3)*(sin(Pi/6)+sin(Pi/2))^2 = (4/3)*(1/2+1)^2 = (4/3)*(9/4) = 3.

%e n=2 (4/3)*(sin(Pi/3)+sin(Pi))^2 = (4/3)*(((3)^.5)/2+0)^2 = (4/3)*(3/4) = 1.

%e n=3 (4/3)*(sin(Pi/2)+sin(3*Pi/2))^2 = (4/3)*(1-1)^2 = 0.

%e n=4 (4/3)*(sin(2*Pi/3)+sin(2*Pi))^2 = (4/3)*(((3)^.5)/2+0)^2 = (4/3)*(3/4) = 1.

%e n=5 (4/3)*(sin(5*Pi/6)+sin(5*Pi/2))^2 = (4/3)*(1/2+1)^2 = (4/3)*(9/4) = 3.

%p P:=proc(n) local i,j; for i from 0 by 1 to n do j:=4/3*(sin(i*Pi/6)+sin(i*Pi/2))^2; print(j); od; end: P(20);

%K easy,nonn

%O 0,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 21 2006