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Problem 1845. Pascal's pyramid

Created by Tim

In Pascal's triangle each number is the sum of the two nearest numbers in the line above:

           1
         1   1
       1   2   1
     1   3   3   1
   1   4   6   4   1

A three-dimensional analog of Pascal's triangle can be defined as a square pyramid in which each number is the sum of the four nearest numbers in the layer above. Define a function pascalp(n) that returns the nth layer of this pyramid, as follows:

   pascalp(1)
      1
   pascalp(2)
      1  1
      1  1
   pascalp(3)
      1  2  1
      2  4  2
      1  2  1
   pascalp(4)
      1  3  3  1
      3  9  9  3
      3  9  9  3
      1  3  3  1
   pascalp(5)
      1  4  6  4 1
      4 16 24 16 4
      6 24 36 24 6
      4 16 24 16 4
      1  4  6  4 1

Note: Pascal's pyramid can also be defined as a tetrahedron (see http://en.wikipedia.org/wiki/Pascal%27s_pyramid), in which case the layers are triangular rather than square, and the numbers are the trinomial coefficients.

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22 correct solutions 7 incorrect solutions
Last solution submitted on Sep 17, 2014

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