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Is this sum exponential?

  1. Jul 16, 2009 #1

    I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?"

    Anyway, during solving this problem I came to this point:

    Is the following sum exponential in [itex]2n[/itex]?

    \sum_{x=0}^{n} \left( \begin{array}{cc} 2n \\ 2x \end{array} \right)

    Are there some nice combinatorial identities which I overlooked that can be useful in this case?

    Thank you very much.
  2. jcsd
  3. Jul 16, 2009 #2


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    Science Advisor

    If you leave out the 2's in the combinatorial symbol, the answer (as you probably know) is 2n. I would guess your sum is something like 2(2n-1), since you are missing about half the terms.
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