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Reduce the sequenceor how to calculate it efficiently

  1. Jul 5, 2012 #1
    Sequence is
    (in Summation notation)
    SUMMATION[from k=0 to k=floor(n/2)] (n-k)C(k) * 2(n-k-1)
    refer to this image
    after expanding it becomes
    (n)C(0)*2(n-1) + (n-1)C(1)*2(n-2) + (n-2)C(2) * 2(n-3) +....
    I want to calculate the value of function for a large value of n(up to
    1010, and ans is to be found MODULUS to some prime number..like

    Please simplify the series if possible or let me know the way how to
    solve it efficiently.
  2. jcsd
  3. Jul 5, 2012 #2
    Mathematica code

    Code (Text):
    Sum[Binomial[n - k, k]*2^(n - k - 1), {k, 0, Floor[n/2]}]
    you can use wolfram alpha to evaluate the exact form, if you don't have mathematica installed.

    answer is attached

    Attached Files:

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