text: 
  # -*- coding: utf-8 -*-
  '''
      File name: code\quintinomial_coefficients\sol_588.py
      Author: Vaidic Joshi
      Date created: Oct 20, 2018
      Python Version: 3.x
  '''
  
  # Solution to Project Euler Problem #588 :: Quintinomial coefficients
  # 
  # For more information see:
  # https://projecteuler.net/problem=588
  
  # Problem Statement 
  '''
  The coefficients in the expansion of $(x+1)^k$ are called binomial coefficients.
  Analoguously the coefficients in the expansion of $(x^4+x^3+x^2+x+1)^k$ are called quintinomial coefficients. (quintus= Latin for fifth).
  
  
  Consider the expansion of $(x^4+x^3+x^2+x+1)^3$:
  $x^{12}+3x^{11}+6x^{10}+10x^9+15x^8+18x^7+19x^6+18x^5+15x^4+10x^3+6x^2+3x+1$
  As we can see 7 out of the 13 quintinomial coefficients for $k=3$ are odd.
  
  
  Let $Q(k)$ be the number of odd coefficients in the expansion of $(x^4+x^3+x^2+x+1)^k$.
  So $Q(3)=7$.
  
  
  You are given $Q(10)=17$ and $Q(100)=35$.
  
  Find  $\sum_{k=1}^{18}Q(10^k) $.
  '''
  
  # Solution 
  
  # Solution Approach 
  '''
  '''
  