#!/usr/bin/env python

"""

series.py

solutions to the Fibonacci Series and Lucas numbers

"""

def fibonacci(n):

""" compute the nth Fibonacci number """

if n < 0:

return None

elif n == 0:

return 0

if n == 1:

return 1

else:

return fibonacci(n - 1) + fibonacci(n - 2)

def lucas(n):

""" compute the nth Lucas number """

if n < 0:

return None

if n == 0:

return 2

elif n == 1:

return 1

else:

return lucas(n - 1) + lucas(n - 2)

def sum_series(n, n0=0, n1=1):

"""

compute the nth value of a summation series.

:param n0=0: value of zeroth element in the series

:param n1=1: value of first element in the series

if n0 == 0 and n1 == 1, the result is the Fibbonacci series

if n0 == 2 and n1 == 1, the result is the Lucas series

"""

if n < 0:

return None

if n == 0:

return n0

elif n == 1:

return n1

else:

return sum_series(n - 1, n0, n1) + sum_series(n - 2, n0, n1)

if __name__ == "__main__":

# run some tests

assert fibonacci(-1) is None

assert fibonacci(-23) is None

assert fibonacci(0) == 0

assert fibonacci(1) == 1

assert fibonacci(2) == 1

assert fibonacci(3) == 2

assert fibonacci(4) == 3

assert fibonacci(5) == 5

assert fibonacci(6) == 8

assert fibonacci(7) == 13

assert lucas(-1) is None

assert lucas(-23) is None

# do these with a loop:

tests = [(0, 2),

(1, 1),

(2, 3),

(3, 4),

(4, 7),

(5,11),

(6,18),

(7, 29),

]

for input, output in tests:

assert lucas(input) == output

# test if sum_series matched Fibonacci

for n in range(0, 10):

assert sum_series(n) == fibonacci(n)

# test if sum_series matched lucas

for n in range(0, 10):

assert sum_series(n, 2, 1) == lucas(n)

print "tests passed"