A120323 Periodic sequence 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, 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, 1, 0, 1, 3, 0, 3, 1, 0, 1, 3, 0, 3, 1, 0, 1, 3, 0

Offset

0,2

Links

Table of n, a(n) for n=0..78.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Formula

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

Example

n=0 (4/3)*(sin(0)+sin(0))^2 = 0.
n=1 (4/3)*(sin(Pi/6)+sin(Pi/2))^2 = (4/3)*(1/2+1)^2 = (4/3)*(9/4) = 3.
n=2 (4/3)*(sin(Pi/3)+sin(Pi))^2 = (4/3)*(((3)^.5)/2+0)^2 = (4/3)*(3/4) = 1.
n=3 (4/3)*(sin(Pi/2)+sin(3*Pi/2))^2 = (4/3)*(1-1)^2 = 0.
n=4 (4/3)*(sin(2*Pi/3)+sin(2*Pi))^2 = (4/3)*(((3)^.5)/2+0)^2 = (4/3)*(3/4) = 1.
n=5 (4/3)*(sin(5*Pi/6)+sin(5*Pi/2))^2 = (4/3)*(1/2+1)^2 = (4/3)*(9/4) = 3.

Maple

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);

Crossrefs

Sequence in context: A308243 A268386 A122779 * A320476 A304326 A099905

Adjacent sequences: A120320 A120321 A120322 * A120324 A120325 A120326

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 21 2006

Status

approved