binary_sequences

int countBinarySequences(int n, int k) {

  /*
   * vector<int> dp (short for dynamic programming)
   * is used for storing the interim values.
   */
  std::vector<int> dp(k, 0);
  dp[0] = 1;

  for (int i = 0; i <= n; i++) {
    int sum = dp[0];
    for (int j = k - 1; j > 0; j--) {
      sum += dp[j];
      dp[j] = dp[j+1] ;
    }
    dp[0] = sum;
  }
  return dp[0];
}