"""
Starting with the number 1 and moving to the right in a clockwise direction a 5
by 5 spiral is formed as follows:
21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
It can be verified that the sum of the numbers on the diagonals is 101.
What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed
in the same way?
"""
from math import ceil
def diagonal_sum(n):
"""Returns the sum of the numbers on the diagonals in a n by n spiral
formed in the same way.
>>> diagonal_sum(1001)
669171001
>>> diagonal_sum(500)
82959497
>>> diagonal_sum(100)
651897
>>> diagonal_sum(50)
79697
>>> diagonal_sum(10)
537
"""
total = 1
for i in range(1, int(ceil(n / 2.0))):
odd = 2 * i + 1
even = 2 * i
total = total + 4 * odd ** 2 - 6 * even
return total
if __name__ == "__main__":
import sys
if len(sys.argv) == 1:
print(diagonal_sum(1001))
else:
try:
n = int(sys.argv[1])
print(diagonal_sum(n))
except ValueError:
print("Invalid entry - please enter a number")