// PROGRAM ID:  fibonacci.cpp / Fibonacci Number Sequence Generator
// REMARKS:  Leonardo of Pisa, who is also called Leonardo Fibonacci,
// originated the following sequence of numbers in the year 1202:
// 0, 1, 1, 2, 3, 5, 8, 13, 21,...  In this sequence, each number is
// the sum of the preceding two and is denoted by F 
// (F for Fibonacci and n for number).             n
// 
// Formally, this sequence is defined as                                      
// 
//                   F    = 0                                              
//                    1                                                    
//
//                   F    = 1                                              
//                    2                                                    
//
//                   F    = F    + F     where n>=1                        
//                    n+2    n+1    n                                      
//
// This program prints the first NUMBER_TO_PRINT Fibonacci numbers.
//  .    1    .    2    .    3    .    4    .    5    .    6    .    7    .
//3456789012345678901234567890123456789012345678901234567890123456789012345
                                                                        
#include <iostream>
using namespace std;

const int NUMBER_TO_PRINT=20; // How many Fibonacci numbers to print

int main()
{
	int current;          // Current Fibonacci number being calculated
	int firstPrevious;    // Previous Fibonacci number in sequence
	int secondPrevious;   // 2nd Previous Fibonacci number in sequence
	int counter;          // Count of how many numbers printed

	// Initialize 
	cout <<  "Fibonacci Number Sequence \n\n";
	secondPrevious = 0;
	firstPrevious  = 1;
	cout << secondPrevious << endl << firstPrevious << endl;
	counter = 2;

	// Generate and print remaining Fibonacci numbers 
	while (counter < NUMBER_TO_PRINT)
	{
		current = firstPrevious + secondPrevious;
		cout << current << endl;
		counter++;
		secondPrevious = firstPrevious;
		firstPrevious = current;
	}

	return 0;
} // end main