Describing an odd/even series

  1. I hope the title is not too confusing. I couldn't think how to summarize this problem.

    If n=2, c=2 (sum of 1+1)
    If n=3, c=3 (sum of 1+1+1)
    If n=4, c=5 (sum of 1+2+1+1)
    If n=5, c=7 (sum of 1+2+2+1+1)
    If n=6, c=10 (sum of 1+2+3+2+1+1)

    My issue is, what is c in terms of n?

    So far I've had an idea:

    I could propose c=(n2/4)+1, but now I need some way of removing the extra 0.25 that crops up for all odd values of n. What I need now is a little piece which =-0.25 if n is odd and =0 if n is even.

    Since (-1)n=-1 if n is odd and 0n=0, I would appreciate a function b of n such that c=(n2/4)+(b)n*0.25. b would evaluate to -1 if n is odd and 0 if n is even.

    Alternatively any solution would be welcomed!

    Edit: I've solved it, don't worry. [SOLVED]
    Last edited: Apr 27, 2013
  2. jcsd
  3. Nugatory

    Staff: Mentor

    How about [itex]-(\frac{1+(-1)^{n+1}}{8})[/itex]
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