Generates a sequence of triangle numbers

triangle_dict.py

# Copyright 2013, Alex Ausch 
# Free to use under attribution license: http://creativecommons.org/licenses/by/2.0/ca/

try:
    from collections.abc import Mapping
except ImportError:
    from collections import Mapping
 
 
class TriangleDictionary(Mapping):
    """A TriangleDictionary maps triangle numbers to their place in their generation sequence:
 
        >>> p = TriangleDictionary()
        >>> p[1]
        1
        >>> p[3]
        6
        >>> p[7]
        28
        >>> 4 in p
        10
 
    The object generates triangle numbers as needed. When iterated over, it
    yields the numbers generated so far:
 
        >>> 11 in p
        True
        >>> list(p)
        [1,3,6,10,15,21,28,36,45,55,66]
 
    """
    instance = None
    def __new__(cls):
        if cls.instance is None:
            cls.instance = super(TriangleDictionary, cls).__new__(cls)
        return cls.instance
 
    def __init__(self):
        super(TriangleDictionary, self).__init__()
        self.inner_dict = {}
        self.inner_dict[1] = 1

    def __iter__(self):
        return iter(self.inner_dict.values())

    def __len__(self):
        return len(self.inner_dict)
 
    def __contains__(self, key):
        try:
            key = int(key)
        except ValueError:
            return False
        if key < 1: return False
        if not key in self.inner_dict:
            self[key]
        return True
 
    def __setitem__(self, key, value):
       raise TypeError("'TriangleDictionary' object doesn't support item assignment")
 
    def __delitem__(self, key):
        raise TypeError("'TriangleDictionary' object doesn't support item removal")
  
    def __getitem__(self,key):
        try:
            key = int(key)
        except:
            return False
        if key > len (self):            
           self.inner_dict[key] = key + self[key - 1] #more useful than 1/2key(key+1), depending on application
        return self.inner_dict[key]