<gh_stars>1-10

# -*- coding: utf-8 -*-
'''
    File name: code\gcd_and_tiling\sol_440.py
    Author: <NAME>
    Date created: Oct 20, 2018
    Python Version: 3.x
'''

# Solution to Project Euler Problem #440 :: GCD and Tiling
# 
# For more information see:
# https://projecteuler.net/problem=440

# Problem Statement 
'''
We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:

For example, here are some of the ways to tile a board of length n = 8:

Let T(n) be the number of ways to tile a board of length n as described above.

For example, T(1) = 10 and T(2) = 101.

Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L.
For example:
S(2) = 10444
S(3) = 1292115238446807016106539989
S(4) mod 987 898 789 = 670616280.

Find S(2000) mod 987 898 789.
'''

# Solution 

# Solution Approach 
'''
'''

# -*- coding: utf-8 -*-
'''
    File name: code\gcd_and_tiling\sol_440.py
    Author: <NAME>
    Date created: Oct 20, 2018
    Python Version: 3.x
'''

# Solution to Project Euler Problem #440 :: GCD and Tiling
# 
# For more information see:
# https://projecteuler.net/problem=440

# Problem Statement 
'''
We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:

For example, here are some of the ways to tile a board of length n = 8:

Let T(n) be the number of ways to tile a board of length n as described above.

For example, T(1) = 10 and T(2) = 101.

Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L.
For example:
S(2) = 10444
S(3) = 1292115238446807016106539989
S(4) mod 987 898 789 = 670616280.

Find S(2000) mod 987 898 789.
'''

# Solution 

# Solution Approach 
'''
'''
# -*- coding: utf-8 -*- File name: code\gcd_and_tiling\sol_440.py     Author: <NAME>     Date created: Oct 20, 2018     Python Version: 3.x # Solution to Project Euler Problem #440 :: GCD and Tiling # # For more information see: # https://projecteuler.net/problem=440 # Problem Statement We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:  For example, here are some of the ways to tile a board of length n = 8:  Let T(n) be the number of ways to tile a board of length n as described above.  For example, T(1) = 10 and T(2) = 101.  Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L. For example: S(2) = 10444 S(3) = 1292115238446807016106539989 S(4) mod 987 898 789 = 670616280.  Find S(2000) mod 987 898 789. # Solution # Solution Approach