# [JAVA] A rudimentary note on the Fibonacci sequence

・ Fibonacci sequence

The ** Fibonacci sequence ** is a sequence derived from the "Rabbit Arithmetic" conceived by the Italian mathematician Leonardo Fibonacci. This sequence appears in many phenomena in the natural world, and it is said that the law of ** Fibonacci sequence ** works on the sequence of sunflower seeds.

When the nth Fibonacci number is represented by Fn, Fn recursively

``````F0 = 0
F1 = 1

Fn+2 = Fn + Fn+1　(n≧0)
``````

Defined in.

The sum of the first and second values ​​gives the third value. In other words, the number obtained by adding the previous value and the previous two values ​​is the next number.

・ Code actually written

``````public class TryJava0120 {

public static void main(String[] args) {

int f0, f1, fn;

f0 = 0;
System.out.println("f0= " + f0);

f1 = 1;
System.out.println("f1= " + f1);

for (int i = 2; i <= 20; i++) {
fn = f0 + f1;

System.out.println(fn);
f0 = f1;
f1 = fn;

System.out.println(f0 + " + " + f1 + "Is");
}

}

}
``````

·Execution result
``````f0= 0
f1= 1
1
1 +1 is
2
1 +2 is
3
2 +3 is
5
3 +5 is
8
5 +8 is
13
8 +13 is
21
13 +21 is
34
21 +34 is
55
34 +55 is
89
55 +89 is
144
89 +144 is
233
144 +233 is
377
233 +377 is
610
377 +610 is
987
610 +987 is
1597
987 +1597 is
2584
1597 +2584 is
4181
2584 +4181 is
6765
4181 +6765 is
``````

The value is assigned to the variable fn and output as equal to the calculation result (f0) of the previous calculation + the previous calculation result (f1).