Problem 1845. Pascal's pyramid

Created by Tim

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In Pascal's triangle each number is the sum of the two nearest numbers in the line above:<pre> 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1</pre>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 <tt>pascalp(n)</tt> that returns the nth layer of this pyramid, as follows:<pre> 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</pre>Note: Pascal's pyramid can also be defined as a tetrahedron (see <a href = "http://en.wikipedia.org/wiki/Pascal%27s_pyramid">http://en.wikipedia.org/wiki/Pascal%27s_pyramid</a>), in which case the layers are triangular rather than square, and the numbers are the trinomial coefficients.

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Solution 309847

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Andrew Newell on 24 Aug 2013

Beautiful!

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Problem 1845. Pascal's pyramid

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