Problem 1845. Pascal's pyramid
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
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers110
Suggested Problems
-
1753 Solvers
-
Calculate the area of a triangle between three points
3170 Solvers
-
754 Solvers
-
Decimation - Optimized for speed
185 Solvers
-
Find the sides of an isosceles triangle when given its area and height from its base to apex
1987 Solvers
More from this Author11
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!