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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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Last solution submitted on May 07, 2015

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