r"""
Python module for OEIS sequence number A070868.

a(1) = a(2) = 1; for n > 2, a(n) = a(a(n-1)) + a(n+1 - 2*a(n-1)).

Examples of use.
-----------------------------------------------------------------------
>>> from a070868 import *
>>> print a070868_list(18)
[1, 1, 2, 2, 2, 3, 3, 4, 3, 4, 4, 4, 5, 4, 6, 5, 6, 6]
>>> print a070868_offset
1
>>> for x in a070868_list_pairs(6):
...     print x
...
(1, 1)
(2, 1)
(3, 2)
(4, 2)
(5, 2)
(6, 3)
>>> print a070868(100)
20
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a070868_offset', 'a070868_list', 'a070868_list_pairs', 'a070868', 'a070868_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a070868_offset = offset = 1

def a070868_gen():
    """Generator function for OEIS sequence A070868."""
    a = {1:1, 2:1}
    yield a[1]
    yield a[2]
    for n in count(3):
        a[n] = a[a[n-1]] + a[n+1 - 2*a[n-1]]
        yield a[n]

def a070868_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(a070868_gen(), n))

def a070868_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), a070868_gen()))

def a070868(n):
    """Returns the term with index n >= 1; offset 1."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a070868_gen(), n-offset, n-offset+1)).pop()