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pascals-triangle.py
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# I was facinated by the pascal's triangle and wanted to play around with it.. I wanted to test out a few things on the larger scale
# and foudn this code online at http://stackoverflow.com/questions/24093387/pascals-triangle-for-python
# Made a few changes and it now prints it beautifully
import math,sys
# pascals_tri_formula = [] # don't collect in a global variable.
def combination(n, r): # correct calculation of combinations, n choose k
return int((math.factorial(n)) / ((math.factorial(r)) * math.factorial(n - r)))
def for_test(x, y): # don't see where this is being used...
for y in range(x):
return combination(x, y)
def pascals_triangle(rows):
result = [] # need something to collect our results in
# count = 0 # avoidable! better to use a for loop,
# while count <= rows: # can avoid initializing and incrementing
for count in range(rows): # start at 0, up to but not including rows number.
# this is really where you went wrong:
row = [] # need a row element to collect the row in
for element in range(count + 1):
# putting this in a list doesn't do anything.
# [pascals_tri_formula.append(combination(count, element))]
row.append((combination(count, element))%7)
result.append(row)
# count += 1 # avoidable
return result
# now we can print a result:
count = 50 ## Prints for 50 rows
for row in pascals_triangle(50):
sys.stdout.write(" "*count)
for i in row:
sys.stdout.write(str(i) + " ")
sys.stdout.write("\n")
count-=1
## OUTPUT FROM THE PROGRAM
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 3 3 5 1
1 6 1 6 1 6 1
1 0 0 0 0 0 0 1
1 1 0 0 0 0 0 1 1
1 2 1 0 0 0 0 1 2 1
1 3 3 1 0 0 0 1 3 3 1
1 4 6 4 1 0 0 1 4 6 4 1
1 5 3 3 5 1 0 1 5 3 3 5 1
1 6 1 6 1 6 1 1 6 1 6 1 6 1
1 0 0 0 0 0 0 2 0 0 0 0 0 0 1
1 1 0 0 0 0 0 2 2 0 0 0 0 0 1 1
1 2 1 0 0 0 0 2 4 2 0 0 0 0 1 2 1
1 3 3 1 0 0 0 2 6 6 2 0 0 0 1 3 3 1
1 4 6 4 1 0 0 2 1 5 1 2 0 0 1 4 6 4 1
1 5 3 3 5 1 0 2 3 6 6 3 2 0 1 5 3 3 5 1
1 6 1 6 1 6 1 2 5 2 5 2 5 2 1 6 1 6 1 6 1
1 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 1
1 1 0 0 0 0 0 3 3 0 0 0 0 0 3 3 0 0 0 0 0 1 1
1 2 1 0 0 0 0 3 6 3 0 0 0 0 3 6 3 0 0 0 0 1 2 1
1 3 3 1 0 0 0 3 2 2 3 0 0 0 3 2 2 3 0 0 0 1 3 3 1
1 4 6 4 1 0 0 3 5 4 5 3 0 0 3 5 4 5 3 0 0 1 4 6 4 1
1 5 3 3 5 1 0 3 1 2 2 1 3 0 3 1 2 2 1 3 0 1 5 3 3 5 1
1 6 1 6 1 6 1 3 4 3 4 3 4 3 3 4 3 4 3 4 3 1 6 1 6 1 6 1
1 0 0 0 0 0 0 4 0 0 0 0 0 0 6 0 0 0 0 0 0 4 0 0 0 0 0 0 1
1 1 0 0 0 0 0 4 4 0 0 0 0 0 6 6 0 0 0 0 0 4 4 0 0 0 0 0 1 1
1 2 1 0 0 0 0 4 1 4 0 0 0 0 6 5 6 0 0 0 0 4 1 4 0 0 0 0 1 2 1
1 3 3 1 0 0 0 4 5 5 4 0 0 0 6 4 4 6 0 0 0 4 5 5 4 0 0 0 1 3 3 1
1 4 6 4 1 0 0 4 2 3 2 4 0 0 6 3 1 3 6 0 0 4 2 3 2 4 0 0 1 4 6 4 1
1 5 3 3 5 1 0 4 6 5 5 6 4 0 6 2 4 4 2 6 0 4 6 5 5 6 4 0 1 5 3 3 5 1
1 6 1 6 1 6 1 4 3 4 3 4 3 4 6 1 6 1 6 1 6 4 3 4 3 4 3 4 1 6 1 6 1 6 1
1 0 0 0 0 0 0 5 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 5 0 0 0 0 0 0 1
1 1 0 0 0 0 0 5 5 0 0 0 0 0 3 3 0 0 0 0 0 3 3 0 0 0 0 0 5 5 0 0 0 0 0 1 1
1 2 1 0 0 0 0 5 3 5 0 0 0 0 3 6 3 0 0 0 0 3 6 3 0 0 0 0 5 3 5 0 0 0 0 1 2 1
1 3 3 1 0 0 0 5 1 1 5 0 0 0 3 2 2 3 0 0 0 3 2 2 3 0 0 0 5 1 1 5 0 0 0 1 3 3 1
1 4 6 4 1 0 0 5 6 2 6 5 0 0 3 5 4 5 3 0 0 3 5 4 5 3 0 0 5 6 2 6 5 0 0 1 4 6 4 1
1 5 3 3 5 1 0 5 4 1 1 4 5 0 3 1 2 2 1 3 0 3 1 2 2 1 3 0 5 4 1 1 4 5 0 1 5 3 3 5 1
1 6 1 6 1 6 1 5 2 5 2 5 2 5 3 4 3 4 3 4 3 3 4 3 4 3 4 3 5 2 5 2 5 2 5 1 6 1 6 1 6 1
1 0 0 0 0 0 0 6 0 0 0 0 0 0 1 0 0 0 0 0 0 6 0 0 0 0 0 0 1 0 0 0 0 0 0 6 0 0 0 0 0 0 1
1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1
1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1
1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1
1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1
1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 3 3 5 1
1 6 1 6 1 6 1
1 0 0 0 0 0 0 1
1 1 0 0 0 0 0 1 1
1 2 1 0 0 0 0 1 2 1
1 3 3 1 0 0 0 1 3 3 1
1 4 6 4 1 0 0 1 4 6 4 1
1 5 3 3 5 1 0 1 5 3 3 5 1
1 6 1 6 1 6 1 1 6 1 6 1 6 1
1 0 0 0 0 0 0 2 0 0 0 0 0 0 1
1 1 0 0 0 0 0 2 2 0 0 0 0 0 1 1
1 2 1 0 0 0 0 2 4 2 0 0 0 0 1 2 1
1 3 3 1 0 0 0 2 6 6 2 0 0 0 1 3 3 1
1 4 6 4 1 0 0 2 1 5 1 2 0 0 1 4 6 4 1
1 5 3 3 5 1 0 2 3 6 6 3 2 0 1 5 3 3 5 1
1 6 1 6 1 6 1 2 5 2 5 2 5 2 1 6 1 6 1 6 1
1 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 1
1 1 0 0 0 0 0 3 3 0 0 0 0 0 3 3 0 0 0 0 0 1 1
1 2 1 0 0 0 0 3 6 3 0 0 0 0 3 6 3 0 0 0 0 1 2 1
1 3 3 1 0 0 0 3 2 2 3 0 0 0 3 2 2 3 0 0 0 1 3 3 1
1 4 6 4 1 0 0 3 5 4 5 3 0 0 3 5 4 5 3 0 0 1 4 6 4 1
1 5 3 3 5 1 0 3 1 2 2 1 3 0 3 1 2 2 1 3 0 1 5 3 3 5 1
1 6 1 6 1 6 1 3 4 3 4 3 4 3 3 4 3 4 3 4 3 1 6 1 6 1 6 1
1 0 0 0 0 0 0 4 0 0 0 0 0 0 6 0 0 0 0 0 0 4 0 0 0 0 0 0 1
1 1 0 0 0 0 0 4 4 0 0 0 0 0 6 6 0 0 0 0 0 4 4 0 0 0 0 0 1 1
1 2 1 0 0 0 0 4 1 4 0 0 0 0 6 5 6 0 0 0 0 4 1 4 0 0 0 0 1 2 1
1 3 3 1 0 0 0 4 5 5 4 0 0 0 6 4 4 6 0 0 0 4 5 5 4 0 0 0 1 3 3 1
1 4 6 4 1 0 0 4 2 3 2 4 0 0 6 3 1 3 6 0 0 4 2 3 2 4 0 0 1 4 6 4 1
1 5 3 3 5 1 0 4 6 5 5 6 4 0 6 2 4 4 2 6 0 4 6 5 5 6 4 0 1 5 3 3 5 1
1 6 1 6 1 6 1 4 3 4 3 4 3 4 6 1 6 1 6 1 6 4 3 4 3 4 3 4 1 6 1 6 1 6 1
1 0 0 0 0 0 0 5 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 5 0 0 0 0 0 0 1
1 1 0 0 0 0 0 5 5 0 0 0 0 0 3 3 0 0 0 0 0 3 3 0 0 0 0 0 5 5 0 0 0 0 0 1 1
1 2 1 0 0 0 0 5 3 5 0 0 0 0 3 6 3 0 0 0 0 3 6 3 0 0 0 0 5 3 5 0 0 0 0 1 2 1
1 3 3 1 0 0 0 5 1 1 5 0 0 0 3 2 2 3 0 0 0 3 2 2 3 0 0 0 5 1 1 5 0 0 0 1 3 3 1
1 4 6 4 1 0 0 5 6 2 6 5 0 0 3 5 4 5 3 0 0 3 5 4 5 3 0 0 5 6 2 6 5 0 0 1 4 6 4 1
1 5 3 3 5 1 0 5 4 1 1 4 5 0 3 1 2 2 1 3 0 3 1 2 2 1 3 0 5 4 1 1 4 5 0 1 5 3 3 5 1
1 6 1 6 1 6 1 5 2 5 2 5 2 5 3 4 3 4 3 4 3 3 4 3 4 3 4 3 5 2 5 2 5 2 5 1 6 1 6 1 6 1
1 0 0 0 0 0 0 6 0 0 0 0 0 0 1 0 0 0 0 0 0 6 0 0 0 0 0 0 1 0 0 0 0 0 0 6 0 0 0 0 0 0 1
1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1 0 0 0 0 0 6 6 0 0 0 0 0 1 1
1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1 0 0 0 0 6 5 6 0 0 0 0 1 2 1
1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1 0 0 0 6 4 4 6 0 0 0 1 3 3 1
1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1 0 0 6 3 1 3 6 0 0 1 4 6 4 1
1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1 0 6 2 4 4 2 6 0 1 5 3 3 5 1
1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1
1 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1
1 4 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 6 4 1
1 5 3 3 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 3 3 5 1
1 6 1 6 1 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 1 6 1 6 1
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1
1 2 1 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 1 2 1
1 3 3 1 0 0 0 1 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 0 0 0 1 3 3 1
1 4 6 4 1 0 0 1 4 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 6 4 1 0 0 1 4 6 4 1
1 5 3 3 5 1 0 1 5 3 3 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 3 3 5 1 0 1 5 3 3 5 1
1 6 1 6 1 6 1 1 6 1 6 1 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 1 6 1 6 1 1 6 1 6 1 6 1
1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1
1 1 0 0 0 0 0 2 2 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 2 2 0 0 0 0 0 1 1
1 2 1 0 0 0 0 2 4 2 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 2 4 2 0 0 0 0 1 2 1
1 3 3 1 0 0 0 2 6 6 2 0 0 0 1 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 0 0 0 2 6 6 2 0 0 0 1 3 3 1
1 4 6 4 1 0 0 2 1 5 1 2 0 0 1 4 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 6 4 1 0 0 2 1 5 1 2 0 0 1 4 6 4 1
1 5 3 3 5 1 0 2 3 6 6 3 2 0 1 5 3 3 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 3 3 5 1 0 2 3 6 6 3 2 0 1 5 3 3 5 1
1 6 1 6 1 6 1 2 5 2 5 2 5 2 1 6 1 6 1 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 1 6 1 6 1 2 5 2 5 2 5 2 1 6 1 6 1 6 1