Khayyam Triangle

# Double Gold Star

# Khayyam Triangle

# The French mathematician, Blaise Pascal, who built a mechanical computer in
# the 17th century, studied a pattern of numbers now commonly known in parts of
# the world as Pascal's Triangle (it was also previously studied by many Indian,
# Chinese, and Persian mathematicians, and is known by different names in other
# parts of the world).

# The pattern is shown below:

#                    1
#                   1 1
#                  1 2 1
#                 1 3 3 1
#                1 4 6 4 1
#                   ...

# Each number is the sum of the number above it to the left and the number above
# it to the right (any missing numbers are counted as 0).

# Define a procedure, triangle(n), that takes a number n as its input, and
# returns a list of the first n rows in the triangle. Each element of the
# returned list should be a list of the numbers at the corresponding row in the
# triangle.


def triangle(n):
    result=[]

    if n==0:
        return result
    if n>=1:
        result.append([1])
    if n > 1:
        i=2
        baseline= [1]
        while i <=n:
            cache= []

            baseline.insert(0,0)
            baseline.insert(len(baseline),0)
            new_baseline=[]
            s=0
            while s < (len(baseline)-1):
                new_baseline.append((baseline[s]+ baseline[s+1]))
                s=s+1
#            print new_baseline
#            cache.append(new_baseline)
            result.append(new_baseline[0:])

            baseline=new_baseline
            i = i+1

    return result







#For example:

print triangle(0)
#>>> []

print triangle(1)
#>>> [[1]]

print triangle(2)
#>> [[1], [1, 1]]

print triangle(3)
#>>> [[1], [1, 1], [1, 2, 1]]

print triangle(6)
#>>> [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1]]