Dynamic Pyramids

Here, for reference, are the two (recursive) methods:

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 );
}

The diagram shows the activation chain when the main() method has called Pyramid(3). This results in three activations of the Pyramid() method. Click on the diagram to see these activations.

When the base case Pyramid(1) is reached, it immediately returns a value of 1. Now the second activation, Pyramid(2), calls Triangle(2) which results in activations of Triangle() added to the chain.

After two activations, Triangle(2), returns a 3 to its caller. Pyramid(2) now has all the values it needs and returns a 4 to its caller.

Pyramid(3) now calls Triangle(3) which eventually returns a 6. The value 10 is returned to main().

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