r"""
Python module for OEIS sequence number A126256.

Number of distinct terms in rows 0 through n of Pascal's triangle.

Examples of use.
-----------------------------------------------------------------------
>>> from a126256 import *
>>> print a126256_list(16)
[1, 1, 2, 3, 5, 7, 9, 12, 16, 20, 24, 29, 35, 41, 48, 53]
>>> print a126256_offset
0
>>> for x in a126256_list_pairs(6):
...     print x
...
(0, 1)
(1, 1)
(2, 2)
(3, 3)
(4, 5)
(5, 7)
>>> print a126256(4)
5
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a126256_offset', 'a126256_list', 'a126256_list_pairs', 'a126256', 'a126256_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a126256_offset = offset = 0

def a126256_gen():
    """Generator function for OEIS sequence A126256."""
    s = set([1])
    for row in count(1):
        yield len(s)
        x = row
        s.add(x)
        for m in xrange(1, row//2 + 1):
            x = (x * (row - m)) / (m + 1)
            s.add(x)

def a126256_list(n):
    """Returns a list of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a126256_gen(), n))

def a126256_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(izip(xrange(offset, n+offset), a126256_gen()))

def a126256(n):
    """Returns the term with index n >= 0; offset 0."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a126256_gen(), n-offset, n-offset+1)).pop()