r"""
Python module for OEIS sequence number A000129.

Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
Also denominators of continued fraction convergents to sqrt(2).

Examples of use.
-----------------------------------------------------------------------
>>> from a000129 import *
>>> print a000129_list(12)
[0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741]
>>> print a000129_offset
0
>>> for x in a000129_list_pairs(6):
...     print x
...
(0, 0)
(1, 1)
(2, 2)
(3, 5)
(4, 12)
(5, 29)
>>> print a000129(5)
29
-----------------------------------------------------------------------
"""

from itertools import islice, izip

__all__ = ('a000129_offset', 'a000129_list', 'a000129_list_pairs', 'a000129', 'a000129_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a000129_offset = offset = 0

def a000129_gen():
    """Generator function for OEIS sequence A000129."""
    x, y = 0, 1
    while True:
        yield x
        x, y = y, 2*y + x

def a000129_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(a000129_gen(), n))

def a000129_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), a000129_gen()))

def a000129(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(a000129_gen(), n-offset, n-offset+1)).pop()