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Pascal's pyramid

  1. Nov 21, 2009 #1
    I have heard that Pascal's pyramid is a 3-dimensional analogue of Pascal's triangle .

    The edges of Pascal's pyramid come from a particular row in Pascal's triangle.

    For example, let's take the row of Pascal's triangle having entries 1 5 10 10 5 1.

    So, the corresponding Pascal's Pyramid is given below.

    1
    5 5
    10 20 10
    10 30 30 10
    5 20 30 20 5
    1 5 10 10 5 1

    Can someone explain how to find the internal entries, such as 20 and 30?

    Thanks.
     
  2. jcsd
  3. Nov 21, 2009 #2
    In general,
    [tex]\frac{(i+j+k)!}{i! j! k!}[/tex]
    You did the ones where [itex]i+j+k=5[/itex]
     
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