For those times you need tuples of non-negative integers to be non-negative integers...

tuple_encoder.py

#!/usr/bin/python
from __future__ import division
import numpy as np

def tuple_encode(x):
    """
    If x is a tuple of non-negative integers, outputs a single non-negative
    integer which is unique for that tuple, based on Cantor's bijection
    argument.
    """
    if len(x) == 1:
        return x
    else:
        i, j = x[0], tuple_encode(x[1:])
        return int((i + j + 1) * (i + j) / 2) + i

def tuple_decode(a, n):
    """
    Given the non-negative integer a, does the inverse operation of
    tuple_encode, assuming the desired tuple has length n.
    """

    if n == 1:
        return [a]
    else:
        # Do not question the voodoo
        b = int(np.floor((1 + np.sqrt(1 + 8 * a)) / 2) - 1)
        j = int(b * (b + 3) / 2 - a)
        i = int((np.sqrt(9 + 8 * (a + j))- 2 * j - 3) / 2)

        return [i] + tuple_decode(j, n - 1)