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Modified Balls in Boxes ; allowi "negative number of balls"

  1. Oct 30, 2015 #1

    WWGD

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    Hi all,

    There is a known formula for the number of solutions to

    ## x_1+x_2+...+x_k =n ## when ##x_1,x_2,...x_n ##are non-negative Integers.

    Question:

    Are there known formulas for the sum ##x_1+x_2+...+x_k =n ##

    when ## x_1, x_2,..,x_k ##

    are positive or negative Integers in a bounded range ## -\infty < m \leq x_i \leq M < \infty ## (redundant) ?

    Thanks.
     
  2. jcsd
  3. Oct 30, 2015 #2

    WWGD

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    Never mind, thanks, just add a constant to each ## x_i## to make each term non-negative and then we refer to usual formula. Please feel free to delete; I asked a very simple/obvious question.
     
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