pyPascalsTriangle

# Pascal's Triangle
# Mike Kerry - 30-Jan-2021 - acclivity2@gmail.com

nrows = int(input("\nHow many rows of Pascal's Triangle would you like to print? "))
nrows = min(nrows, 20)      # restrict it to 20 rows max
print()

row = [0 for _ in range(nrows + nrows + 1)]  # For convenience, we use a row length twice as long as the no. of rows

tri = [row.copy() for _ in range(nrows)]     # We have to use copy() or else we get the same physical row repeated

tri[0][nrows] = 1           # Initialise the triangle with a centrally placed 1 in the top row
maxv = 0
for x in range(1, nrows):
    for y in range(1, nrows + nrows):
        v = tri[x-1][y-1] + tri[x-1][y+1]       # Compute the sum of 2 integers in the higher row, and either side
        tri[x][y] = v
        if v > maxv:
            maxv = v                # Keep a note of the largest integer encountered

width = len(str(maxv))              # find the width required to accommodate the largest integer
for row in tri:
    for x in range(nrows + nrows):
        s = str(row[x])
        if s == "0":                        # 0 entries in our triangle become spaces
            s = " "
        print(s.ljust(width), end="")       # print each integer (or space) with equal width
    print()


# Results:-
# How many rows of Pascal's Triangle would you like to print? 13
#
#                                        1
#                                     1     1
#                                  1     2     1
#                               1     3     3     1
#                            1     4     6     4     1
#                         1     5     10    10    5     1
#                      1     6     15    20    15    6     1
#                   1     7     21    35    35    21    7     1
#                1     8     28    56    70    56    28    8     1
#             1     9     36    84    126   126   84    36    9     1
#          1     10    45    120   210   252   210   120   45    10    1
#       1     11    55    165   330   462   462   330   165   55    11    1
#    1     12    66    220   495   792   924   792   495   220   66    12    1