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 13 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 13. 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
}
}
