Pentagonal Number Theorem - Example Program

Example Program

Here is a simple Python program which computes p(n), the number of partitions, using the recurrence resulting from the pentagonal number theorem.

pentagonal = lambda n : n*(3*n-1)/2 def generalised_pentagonal(n): # 0, 1, -1, 2, -2 if n < 0: return 0 if n%2 == 0: return pentagonal(n/2+1) else: return pentagonal(-(n/2+1)) pt = for n in range (1, 1000+1): r = 0 f = -1 i = 0 while 1: k = generalised_pentagonal(i) if k > n: break if i%2==0: f = -f r += f*pt i += 1 pt.append(r) print pt

Read more about this topic:  Pentagonal Number Theorem

Famous quotes containing the word program:

    “The principal saloon was the Howlin’ Wilderness, an immense log cabin with a log fire always burning in the huge fireplace, where so many fights broke out that the common saying was, “We will have a man for breakfast tomorrow.””
    —For the State of California, U.S. public relief program (1935-1943)

    “Alexander Woollcott broadcasts the story of the wife who returned a dog to the Seeing Eye with this note attached: “I am sending the dog back. My husband used to depend on me. Now he is independent, and I never know where he is.””
    —For the State of New Jersey, U.S. public relief program (1935-1943)