# 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.

### Solution Stats

63.54% Correct | 36.46% Incorrect
Last Solution submitted on Feb 03, 2024

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