public int Pyramid( int N )
{
  if ( N == 1 ) 
  
    return 1;
     
  else
  
    return Pyramid ( N-1 ) + Triangle ( N );
}

Pyramid Program

Here is a complete program that computes Pyramidal numbers. The user specifies N, the number of balls in a side of the base, in the command line.

class Calculate
{
  public int Triangle( int N )
  {
    if ( N == 1 )
      return 1;
    else
      return N + Triangle( N-1 );
  }

  public int Pyramid( int N )
  {
    if ( N == 1 ) 
      return 1;
    else
      return Pyramid ( N-1 ) + Triangle ( N );
  }
}

public class PyramidTester
{
  public static void main ( String[] args)
  {
    int argument = Integer.parseInt( args[0] );

    Calculate calc = new Calculate();
    int result = calc.Pyramid( argument );
    System.out.println("Pyramid(" + argument + ") is " + result );
  }
}

In terms of programming, the requirement that "everything in the definition for Pyramid() is defined someplace" means that the program must include a method for Triangle().

Here is a run of the program:

C:\>java PyramidTester 12
Pyramid(12) is 364