Facebook Hacker Cup - Double Squares Problem

Publishing a coding challenge just for fun. Yup, this is what I do for fun first thing in the morning. I hear one guy did this in 38 characters of Perl.

The challenge is to write a script that will determine how many ways N can be written as the sum of the squares of two nonzero positive integers where N is also a nonzero positive integer. Checking your work, the result for 25 should be 1, 338 should be 2 and 1000000 should be 3. Extra credit for making the algorithm as efficient as possible.

# define function
this.doubleSquareFinder = (number) ->  
  combinations = 0

  # memoize for speed
  doubleSquareFinder.hash = doubleSquareFinder.hash || {}

  if typeof doubleSquareFinder.hash[number] != 'undefined'
    return doubleSquareFinder.hash[number]

  #no need to check numbers larger than what is possible
  range = Math.sqrt number/2
  half = number/2

  # iterate
  for a in [1..range]
    for b in [a..half]
      combinations++ if (a*a + b*b == number)

  doubleSquareFinder.hash[number] = combinations

  return combinations