r"""
Python module for OEIS sequence number A000213.

Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3),
with a(0) = a(1) = a(2) = 1.

Examples of use.
-----------------------------------------------------------------------
>>> from a000213 import *
>>> print a000213_list(15)
[1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201, 2209]
>>> print a000213_offset
0
>>> for x in a000213_list_pairs(6):
...     print x
...
(0, 1)
(1, 1)
(2, 1)
(3, 3)
(4, 5)
(5, 9)
>>> a000213_list_upto(1000)
[1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653]
>>> print a000213(3)
3
-----------------------------------------------------------------------
"""

from itertools import islice, izip, takewhile

__all__ = ('a000213_offset', 'a000213_list', 'a000213_list_pairs', 'a000213_list_upto', 'a000213', 'a000213_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a000213_offset = offset = 0

def a000213_gen():
    """Generator function for OEIS sequence A000213."""
    x = y = z = 1
    while True:
        yield x
        x, y, z = y, z, x + y + z

def a000213_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(a000213_gen(), n))

def a000213_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), a000213_gen()))

def a000213_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, a000213_gen()))

def a000213(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(a000213_gen(), n-offset, n-offset+1)).pop()