1.3 The Fibonacci Series

The Fibonacci numbers are a sequence of numbers in which each successive number is the sum of the two preceding numbers. The sequence begins 1, 1, 2, 3, 5, 8, 13, and goes on from there. This sequence appears in interesting places in nature. For example, the number of petals on most species of flowers is one of the Fibonacci numbers.

Example 1-3 shows a program that computes and displays the first 20 Fibonacci numbers. There are several things to note about the program. First, it again uses a for statement. It also declares and uses variables to hold the previous two numbers in the sequence, so that these numbers can be added together to produce the next number in the sequence.

Example 1-3. Fibonacci.java

package je3.basics;
/**
 * This program prints out the first 20 numbers in the Fibonacci sequence.
 * Each term is formed by adding together the previous two terms in the
 * sequence, starting with the terms 1 and 1.
 **/
public class Fibonacci {
    public static void main(String[  ] args) {
        int n0 = 1, n1 = 1, n2;          // Initialize variables
        System.out.print(n0 + " " +      // Print first and second terms
                         n1 + " ");      // of the series

        for(int i = 0; i < 18; i++) {    // Loop for the next 18 terms
            n2 = n1 + n0;                // Next term is sum of previous two
            System.out.print(n2 + " ");  // Print it out
            n0 = n1;                     // First previous becomes 2nd previous
            n1 = n2;                     // And current number becomes previous
        }
        System.out.println( );            // Terminate the line
    }
}