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How to get the closed form of this recurrence?

  1. Mar 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Hello,

    This expression was derived from a polygon word problem and I need to find a closed form for it with repeated substitution (I think).

    T(k, n) = T(k, n-1) + (k-2)(n-1) + 1



    2. Relevant equations



    3. The attempt at a solution

    Get a pattern like:

    = T(k, n-2) + (k - 2)(2n - 3) - 2 subs.
    = T(k, n-3) + (k - 2)(3n - 6) - 3 subs.
    = T(k, n-4) + (k - 2)(4n - 10) -4 subs.
    .
    .
    .

    I'm not sure how to express the 1, 3, 6, 10 sequence in terms of number of substitutions.
     
  2. jcsd
  3. Mar 4, 2012 #2
    What is the boundary coundition?
    This is what I got so far.
    Assuming T(k, 0) = c

    T(k,n) = n+c+(k-2)*1*2*...(n-1)
     
  4. Mar 5, 2012 #3
    Sorry I wrote the expression wrong; but I got the answer I think, thanks.
     
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