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Find closed formula for the sequence.

  1. Mar 1, 2010 #1
    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. jcsd
  3. Mar 1, 2010 #2

    CRGreathouse

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    Science Advisor
    Homework Helper

    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, [tex]w^k+\bar{w^k}[/tex] is 1, -1, or 2 depending on k mod 3. Etc.

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