r"""
Python module for OEIS sequence number A000179.

Menage numbers: number of permutations s of [0, ..., n-1] such that
s(i) != i and s(i) != i+1 (mod n) for all i.

a(n) = ((n^2-2*n)*a(n-1) + n*a(n-2) - 4(-1)^n)/(n-2) for n >= 4.

Examples of use.
-----------------------------------------------------------------------
>>> from a000179 import *
>>> print a000179_list(12)
[1, 0, 0, 1, 2, 13, 80, 579, 4738, 43387, 439792, 4890741]
>>> print a000179_offset
0
>>> for x in a000179_list_pairs(6):
...     print x
...
(0, 1)
(1, 0)
(2, 0)
(3, 1)
(4, 2)
(5, 13)
>>> a000179_list_upto(10000)
[1, 0, 0, 1, 2, 13, 80, 579, 4738]
>>> print a000179(4)
2
-----------------------------------------------------------------------
"""

from itertools import islice, izip, takewhile, count

__all__ = ('a000179_offset', 'a000179_list', 'a000179_list_pairs', 'a000179_list_upto', 'a000179', 'a000179_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a000179_offset = offset = 0

def a000179_gen():
    """Generator function for OEIS sequence A000179."""
    yield 1
    yield 0
    x, y = 0, 1
    for n in count(4):
        yield x
        x, y = y, (n*(n-2)*y + n*x - 4*(-1)**n) / (n-2)

def a000179_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(a000179_gen(), n))

def a000179_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), a000179_gen()))

def a000179_list_upto(m):
    """Returns a list of all terms not exceeding m >= 0."""
    if m < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(takewhile(lambda t: t <= m, a000179_gen()))

def a000179(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(a000179_gen(), n-offset, n-offset+1)).pop()