index_to_code.py

def M(n, k): # n down, k across in Mahonian number triangle
    if n == 1 and k == 0:
        return 1
    elif n < 0 or k < 0 or k > n*(n-1)/2:
        return 0
    else:
        return M(n, k-1) + M(n-1, k) - M(n-1, k-n)

def index_to_code(index, length, weight):
    n = length
    k = weight
    code = [0]*length
    total = 0
    if index > M(n+1, k): # index too high
        raise ValueError('Index is too high for the given amount of digits and digital sum.')
    while k:
        m = M(n, k)
        if m + total <= index:
            total += m
            code[n-1] += 1
            k -= 1
        elif m + total > index:
            n -= 1
    return code

print(*reversed(index_to_code(69, 5, 5)), sep='')