r"""
Python module for OEIS sequence number A019461.

Add 1, multiply by 1, add 2, multiply by 2, and so on.

Examples of use.
-----------------------------------------------------------------------
>>> from a019461 import *
>>> print a019461_list(14)
[0, 1, 1, 3, 6, 9, 27, 31, 124, 129, 645, 651, 3906, 3913]
>>> print a019461_offset
0
>>> for x in a019461_list_pairs(6):
...     print x
...
(0, 0)
(1, 1)
(2, 1)
(3, 3)
(4, 6)
(5, 9)
>>> print a019461(5)
9
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count
from a019460 import a019460_gen

__all__ = ('a019461_offset', 'a019461_list', 'a019461_list_pairs', 'a019461', 'a019460_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a019461_offset = offset = 0

def a019461_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(a019460_gen(0), n))

def a019461_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), a019460_gen(0)))

def a019461(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(a019460_gen(0), n-offset, n-offset+1)).pop()