# Find closed formula for the sequence.

1. Mar 1, 2010

### jjangub

I have a problem with this question.
The question is "Find closed formula for the sequence 0,1,3,0,1,3,0,1,3...."
It can be written as (0,1,0,0,1,0,0,1,0...)+3*(0,0,1,0,0,1,0,0,1...)
I know the sequence of 0,0,1,0,0,1..., but I do not know how to get the
sequence of 0,1,0,0,1,0...
And is there any easier way to get the sequence of 0,0,1,0,0,1...or 0,1,0,0,1,0...?
Thank you...

2. Mar 1, 2010

### CRGreathouse

Depends on what you're allowed to use, and what techniques you know. In Pari it would be
Code (Text):
[3,0,1][n%3+1]
. The "mod" function would make quick work of it. Complex powers could work: with w a cube root of -1, $$w^k+\bar{w^k}$$ is 1, -1, or 2 depending on k mod 3. Etc.

Edit: The conjugate symbol isn't showing up very well...