##########################################################################
#  Copyright (C) 2006 Jaap Spies, jaapspies@gmail.com
#  Copyright (C) 2006 William Stein, wstein@gmail.com
#
#  Distributed under the terms of the GNU General Public License (GPL):
#
#                  http://www.gnu.org/licenses/
##########################################################################


def fib():
    """
        generates an "infinity" of Fibonacci numbers,
        starting with 0
    """
    x, y = 0, 1
    yield x
    while 1:
        x, y = y, x+y
        yield x
 
f = fib()
a = [f.next() for i in range(1002)]
 
def A000045(n):
    r"""
        returns Fibonacci number with index $n \le 1001$, offset 0,4

        S. Plouffe, Project Gutenberg, The First 1001 Fibonacci Numbers
        http://ibiblio.org/pub/docs/books/gutenberg/etext01/fbncc10.txt
 
        We have one more. Our first Fibonacci number is 0.

    INPUT:
        n -- non negative integer

    OUTPUT:
        integer -- function value

    EXAMPLES:
        sage: A000045(4)
        3

        sage: A000045(10)
        55

        sage: A000045(51)
        20365011074

        sage: A000045(-1)
         

        AUTHOR:
            - Jaap Spies (2007-01-05)
    """
    if n >= 0 and n <= 1001:
        return a[n]


def A000045_list(N):
    r"""
        returns a list of the first $N$ Fibonacci numbers

    INPUT:
        N -- non negative integer

    OUTPUT:
        list -- Fibonacci numbers 

    EXAMPLES:
        sage: A000045_list(9)
        [0, 1, 1, 2, 3, 5, 8, 13, 21]

        sage: A000045_list(0)
        []

        sage: A000045_list(1)
        [0]

        AUTHOR:
            - Jaap Spies (2007-01-05)


    """
    return a[:N]