public class EasyRecursion
{
	public static void main(String[] args)
	{
      System.out.println(line(7, '*') + "\n" +
                         line(10, '+') + "\n" +
                         line(19, 'o') );
      System.out.println();
      System.out.println(triangle(5, '*') + "\n" +
                         triangle(6, '+') + "\n" +
                         triangle(9, 'o') );
      System.out.println();
      System.out.println( sumIntegersTo(7)  +
                          " = " + sigma(7) );
      System.out.println( sumIntegersTo(12)  +
                          " = " + sigma(12) );
	}
	
   public static String line(int length, char symbol)
   {
      if (length < 0)
         throw new RuntimeException("Invalid line length");
         
      if (length == 0)
         return "";
         
      return symbol + line(length - 1, symbol);
   }
   
   public static String triangle(int height, char symbol)
   {
      if (height < 0)
         throw new RuntimeException("Invalid Triangle height");
         
      if (height == 0)
         return "";
         
      return triangle(height - 1, symbol) + 
             "\n" + line(height, symbol);
   }
   
   public static String sumIntegersTo(int n)
   {
      if ( n < 0 )
         throw new RuntimeException("Negative Number");
	   
      if ( n == 0 )
         return "";
         
      if ( n == 1)
         return "1";
         
      return sumIntegersTo(n - 1) + " + " + n;
	}
   
	
	public static int sigma(int n)
	{
		if (n < 0)
			throw new RuntimeException("Number must be >= 0");

      if ( n == 0 )
         return 0;
         
		if ( n == 1 )
			return 1;

		return sigma( n-1 ) + n;
	}
}