r"""
Python module for OEIS sequence number A053461.

a(0) = 0; a(n) = a(n-1) - n^2 if positive and new,
otherwise a(n) = a(n-1) + n^2.
('Recaman transform' (see A005132) of the squares.)

Examples of use.
-----------------------------------------------------------------------
>>> from a053461 import *
>>> print a053461_list(16)
[0, 1, 5, 14, 30, 55, 19, 68, 4, 85, 185, 64, 208, 39, 235, 10]
>>> print a053461_offset
0
>>> for x in a053461_list_pairs(6):
...     print x
...
(0, 0)
(1, 1)
(2, 5)
(3, 14)
(4, 30)
(5, 55)
>>> print a053461(3)
14
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count
from a005132 import a005132_gen

__all__ = ('a053461_offset', 'a053461_list', 'a053461_list_pairs', 'a053461', 'a005132_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a053461_offset = offset = 0

def a053461_list(n):
    """Returns a list of the first n >= 0 terms of OEIS sequence A053461."""
    return list(islice(a005132_gen(x*x for x in count()), n))

def a053461_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), a005132_gen(x*x for x in count())))

def a053461(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(a005132_gen(x*x for x in count()), n, n+1)).pop()