Stream (example)

import java.util.ArrayList;  
import java.util.HashMap;
import java.util.stream.Stream;

/* Objective will require changing to abstract class with one or more abstract methods below */
public class Fibo {
    String name;  // name or title of method
    int size;  // nth sequence
    int hashID;  // counter for hashIDs in hash map
    ArrayList<Long> list;   // captures current Fibonacci sequence
    HashMap<Integer, Object> hash;  // captures each sequence leading to final result

    /*
     Zero parameter constructor uses Telescoping technique to allow setting of the required value nth
     @param: none
     */
    public Fibo() {
        this(20); // telescope to avoid code duplication, using default as 20
    }

    /*
     Construct the nth fibonacci number
     @param: nth number, the value is constrained to 92 because of overflow in a long
     */
    public Fibo(int nth) {
        this.size = nth;
        this.list = new ArrayList<>();
        this.hashID = 0;
        this.hash = new HashMap<>();
        //initialize fibonacci and time mvc
        this.init();
    }

    /*
     This Method should be "abstract"
     Leave method as protected, as it is only authorized to extender of the class
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */
    protected void init() {
        this.name = "Stream";
        Stream.iterate(new long[]{0, 1}, f -> new long[]{f[1], f[0] + f[1]})
            .limit(this.size)
            .forEach(f -> this.setData(f[0]) );
    }

    /*
     Number is added to fibonacci sequence, current state of "list" is added to hash for hashID "num"
     */
    public void setData(long num) {
        list.add(num);
        hash.put(this.hashID++, list.clone());
    }

    /*
     Custom Getter to return last element in fibonacci sequence
     */
    public long getNth() {
        return list.get(this.size - 1);
    }

    /*
     Custom Getter to return last fibonacci sequence in HashMap
     */
    public Object getNthSeq(int i) {
        return hash.get(i);
    }

    /*
     Console/Terminal supported print method
     */
    public void print() {
        System.out.println("Init method = " + this.name);
        System.out.println("fibonacci Number " + this.size + " = " + this.getNth());
        System.out.println("fibonacci List = " + this.list);
        System.out.println("fibonacci Hashmap = " + this.hash);
        for (int i=0 ; i<this.size; i++ ) {
            System.out.println("fibonacci Sequence " + (i+1) + " = " + this.getNthSeq(i));
        }
    }

    /*
    Tester class method.  If this becomes abstract you will not be able to test it directly ...
    Change this method to  call "main" class of each of the extended classes
     */
    static public void main(String[] args) {
        Fibo fib = new Fibo();
        fib.print();
    }
}
Fibo.main(null);
Init method = Stream
fibonacci Number 20 = 4181
fibonacci List = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]
fibonacci Hashmap = {0=[0], 1=[0, 1], 2=[0, 1, 1], 3=[0, 1, 1, 2], 4=[0, 1, 1, 2, 3], 5=[0, 1, 1, 2, 3, 5], 6=[0, 1, 1, 2, 3, 5, 8], 7=[0, 1, 1, 2, 3, 5, 8, 13], 8=[0, 1, 1, 2, 3, 5, 8, 13, 21], 9=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34], 10=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55], 11=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89], 12=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144], 13=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233], 14=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377], 15=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610], 16=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987], 17=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597], 18=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584], 19=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]}
fibonacci Sequence 1 = [0]
fibonacci Sequence 2 = [0, 1]
fibonacci Sequence 3 = [0, 1, 1]
fibonacci Sequence 4 = [0, 1, 1, 2]
fibonacci Sequence 5 = [0, 1, 1, 2, 3]
fibonacci Sequence 6 = [0, 1, 1, 2, 3, 5]
fibonacci Sequence 7 = [0, 1, 1, 2, 3, 5, 8]
fibonacci Sequence 8 = [0, 1, 1, 2, 3, 5, 8, 13]
fibonacci Sequence 9 = [0, 1, 1, 2, 3, 5, 8, 13, 21]
fibonacci Sequence 10 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
fibonacci Sequence 11 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
fibonacci Sequence 12 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
fibonacci Sequence 13 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
fibonacci Sequence 14 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233]
fibonacci Sequence 15 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]
fibonacci Sequence 16 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]
fibonacci Sequence 17 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]
fibonacci Sequence 18 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597]
fibonacci Sequence 19 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
fibonacci Sequence 20 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]

For Loop

import java.util.ArrayList;  
import java.util.HashMap;
import java.util.stream.Stream;

/* Objective will require changing to abstract class with one or more abstract methods below */
public class Fibo {
    String name;  // name or title of method
    int size;  // nth sequence
    int hashID;  // counter for hashIDs in hash map
    ArrayList<Long> list;   // captures current Fibonacci sequence
    HashMap<Integer, Object> hash;  // captures each sequence leading to final result

    /*
     Zero parameter constructor uses Telescoping technique to allow setting of the required value nth
     @param: none
    */
    public Fibo() {
        this(20); // telescope to avoid code duplication, using default as 20
    }

    /*
     Construct the nth fibonacci number
     @param: nth number, the value is constrained to 92 because of overflow in a long
     */
    public Fibo(int nth) {
        this.size = nth;
        this.list = new ArrayList<>();
        this.hashID = 0; // starting with index 0
        this.hash = new HashMap<>();
        // initialize fibonacci and time mvc
        this.init();
    }

    /*
     This Method should be "abstract"
     Leave method as protected, as it is only authorized to extender of the class
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */
    protected void init() {
        this.name = "Stream";
        Stream.iterate(new long[]{0, 1}, f -> new long[]{f[1], f[0] + f[1]})
            .limit(this.size)
            .forEach(f -> this.setData(f[0]) );
    }

    /*
     Number is added to fibonacci sequence, current state of "list" is added to hash for hashID "num"
     */
    public void setData(long num) {
        list.add(num);
        hash.put(this.hashID++, list.clone());
    }

    /*
     Custom Getter to return last element in fibonacci sequence
     */
    public long getNth() {
        return list.get(this.size - 1);
    }

    /*
     Custom Getter to return last fibonacci sequence in HashMap
     */
    public Object getNthSeq(int i) {
        return hash.get(i);
    }

    /*
     Console/Terminal supported print method
     */
    public void print() {
        System.out.println("Init method = " + this.name);
        System.out.println("fibonacci Number " + this.size + " = " + this.getNth());
        System.out.println("fibonacci List = " + this.list);
        System.out.println("fibonacci Hashmap = " + this.hash);
        for (int i=0 ; i<this.size; i++ ) {
            System.out.println("fibonacci Sequence " + (i+1) + " = " + this.getNthSeq(i));
        }
    }

    /*
    Tester class method.  If this becomes abstract you will not be able to test it directly ...
    Change this method to  call "main" class of each of the extended classes
     */
    static public void main(String[] args) {
        FiboForLoop fib = new FiboForLoop(); 
        fib.print();
    }
}

/*
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */

public class FiboForLoop extends Fibo {
    protected void init(){
        this.name = "For Loop";
        int num1 = 0;
        int num2 = 1;
        int num3;

        for(int i = 0; i <= this.size; i++){
            this.setData(num1);
             /* On each iteration, we are assigning second number
             * to the first number and assigning the sum of last two
             * numbers to the second number
             */
            num3 = num1 + num2; 
            num1 = num2;  
            num3 = num3;
        }
    }
}

Fibo.main(null);
Init method = For Loop
fibonacci Number 20 = 1
fibonacci List = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Hashmap = {0=[0], 1=[0, 1], 2=[0, 1, 1], 3=[0, 1, 1, 1], 4=[0, 1, 1, 1, 1], 5=[0, 1, 1, 1, 1, 1], 6=[0, 1, 1, 1, 1, 1, 1], 7=[0, 1, 1, 1, 1, 1, 1, 1], 8=[0, 1, 1, 1, 1, 1, 1, 1, 1], 9=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1], 10=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 11=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 12=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 13=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 14=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 15=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 16=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 17=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 18=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 19=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 20=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
fibonacci Sequence 1 = [0]
fibonacci Sequence 2 = [0, 1]
fibonacci Sequence 3 = [0, 1, 1]
fibonacci Sequence 4 = [0, 1, 1, 1]
fibonacci Sequence 5 = [0, 1, 1, 1, 1]
fibonacci Sequence 6 = [0, 1, 1, 1, 1, 1]
fibonacci Sequence 7 = [0, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 8 = [0, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 9 = [0, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 10 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 11 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 12 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 13 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 14 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 15 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 16 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 17 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 18 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 19 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 20 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

While Loop

import java.util.ArrayList;  
import java.util.HashMap;
import java.util.stream.Stream;

/* Objective will require changing to abstract class with one or more abstract methods below */
public class Fibo {
    String name;  // name or title of method
    int size;  // nth sequence
    int hashID;  // counter for hashIDs in hash map
    ArrayList<Long> list;   // captures current Fibonacci sequence
    HashMap<Integer, Object> hash;  // captures each sequence leading to final result

    /*
     Zero parameter constructor uses Telescoping technique to allow setting of the required value nth
     @param: none
    */
    public Fibo() {
        this(20); // telescope to avoid code duplication, using default as 20
    }

    /*
     Construct the nth fibonacci number
     @param: nth number, the value is constrained to 92 because of overflow in a long
     */
    public Fibo(int nth) {
        this.size = nth;
        this.list = new ArrayList<>();
        this.hashID = 0; // starting with index 0
        this.hash = new HashMap<>();
        // initialize fibonacci and time mvc
        this.init();
    }

    /*
     This Method should be "abstract"
     Leave method as protected, as it is only authorized to extender of the class
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */
    protected void init() {
        this.name = "Stream";
        Stream.iterate(new long[]{0, 1}, f -> new long[]{f[1], f[0] + f[1]})
            .limit(this.size)
            .forEach(f -> this.setData(f[0]) );
    }

    /*
     Number is added to fibonacci sequence, current state of "list" is added to hash for hashID "num"
     */
    public void setData(long num) {
        list.add(num);
        hash.put(this.hashID++, list.clone());
    }

    /*
     Custom Getter to return last element in fibonacci sequence
     */
    public long getNth() {
        return list.get(this.size - 1);
    }

    /*
     Custom Getter to return last fibonacci sequence in HashMap
     */
    public Object getNthSeq(int i) {
        return hash.get(i);
    }

    /*
     Console/Terminal supported print method
     */
    public void print() {
        System.out.println("Init method = " + this.name);
        System.out.println("fibonacci Number " + this.size + " = " + this.getNth());
        System.out.println("fibonacci List = " + this.list);
        System.out.println("fibonacci Hashmap = " + this.hash);
        for (int i=0 ; i<this.size; i++ ) {
            System.out.println("fibonacci Sequence " + (i+1) + " = " + this.getNthSeq(i));
        }
    }

    /*
    Tester class method.  If this becomes abstract you will not be able to test it directly ...
    Change this method to  call "main" class of each of the extended classes
     */
    static public void main(String[] args) {
        FiboWhileLoop fib = new FiboWhileLoop(); 
        fib.print();
    }
}

/*
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */

public class FiboWhileLoop extends Fibo {
    protected void init(){
        this.name = "While Loop";
        int num1 = 0;
        int num2 = 1;
        int num3;
        int i = 0;
        while(i <= this.size){
            this.setData(num1);
            num3 = num1 + num2; 
            num1 = num2;  
            num3 = num3;
            i++;
        }
    }
}

Fibo.main(null);
Init method = While Loop
fibonacci Number 20 = 1
fibonacci List = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Hashmap = {0=[0], 1=[0, 1], 2=[0, 1, 1], 3=[0, 1, 1, 1], 4=[0, 1, 1, 1, 1], 5=[0, 1, 1, 1, 1, 1], 6=[0, 1, 1, 1, 1, 1, 1], 7=[0, 1, 1, 1, 1, 1, 1, 1], 8=[0, 1, 1, 1, 1, 1, 1, 1, 1], 9=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1], 10=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 11=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 12=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 13=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 14=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 15=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 16=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 17=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 18=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 19=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 20=[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}
fibonacci Sequence 1 = [0]
fibonacci Sequence 2 = [0, 1]
fibonacci Sequence 3 = [0, 1, 1]
fibonacci Sequence 4 = [0, 1, 1, 1]
fibonacci Sequence 5 = [0, 1, 1, 1, 1]
fibonacci Sequence 6 = [0, 1, 1, 1, 1, 1]
fibonacci Sequence 7 = [0, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 8 = [0, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 9 = [0, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 10 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 11 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 12 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 13 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 14 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 15 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 16 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 17 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 18 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 19 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
fibonacci Sequence 20 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Recursion

import java.util.ArrayList;  
import java.util.HashMap;
import java.util.stream.Stream;

/* Objective will require changing to abstract class with one or more abstract methods below */
public class Fibo {
    String name;  // name or title of method
    int size;  // nth sequence
    int hashID;  // counter for hashIDs in hash map
    ArrayList<Long> list;   // captures current Fibonacci sequence
    HashMap<Integer, Object> hash;  // captures each sequence leading to final result

    /*
     Zero parameter constructor uses Telescoping technique to allow setting of the required value nth
     @param: none
    */
    public Fibo() {
        this(20); // telescope to avoid code duplication, using default as 20
    }

    /*
     Construct the nth fibonacci number
     @param: nth number, the value is constrained to 92 because of overflow in a long
     */
    public Fibo(int nth) {
        this.size = nth;
        this.list = new ArrayList<>();
        this.hashID = 0; // starting with index 0
        this.hash = new HashMap<>();
        // initialize fibonacci and time mvc
        this.init();
    }

    /*
     This Method should be "abstract"
     Leave method as protected, as it is only authorized to extender of the class
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */
    protected void init() {
        this.name = "Stream";
        Stream.iterate(new long[]{0, 1}, f -> new long[]{f[1], f[0] + f[1]})
            .limit(this.size)
            .forEach(f -> this.setData(f[0]) );
    }

    /*
     Number is added to fibonacci sequence, current state of "list" is added to hash for hashID "num"
     */
    public void setData(long num) {
        list.add(num);
        hash.put(this.hashID++, list.clone());
    }

    /*
     Custom Getter to return last element in fibonacci sequence
     */
    public long getNth() {
        return list.get(this.size - 1);
    }

    /*
     Custom Getter to return last fibonacci sequence in HashMap
     */
    public Object getNthSeq(int i) {
        return hash.get(i);
    }

    /*
     Console/Terminal supported print method
     */
    public void print() {
        System.out.println("Init method = " + this.name);
        System.out.println("fibonacci Number " + this.size + " = " + this.getNth());
        System.out.println("fibonacci List = " + this.list);
        System.out.println("fibonacci Hashmap = " + this.hash);
        for (int i=0 ; i<this.size; i++ ) {
            System.out.println("fibonacci Sequence " + (i+1) + " = " + this.getNthSeq(i));
        }
    }

    /*
    Tester class method.  If this becomes abstract you will not be able to test it directly ...
    Change this method to  call "main" class of each of the extended classes
     */
    static public void main(String[] args) {
        FiboRecursion fib = new FiboRecursion(); 
        fib.print();
    }
}

/*
     Make new class that extends and defines init()
     Inside references within this class would change from this to super
     Repeat process using for, while, recursion
     */

public class FiboRecursion extends Fibo {
    protected void init(){
        this.name = "Recursion";
        for(int i = 0; i <= this.size; i++){
            this.setData(fib(i));
        }
    }

 public static int fib(int i) {
    if ((i == 0) || (i == 1)) {
        return i;
    }
    else{
       return fib(i - 1) + fib(i - 2);
      }
    }
 }


Fibo.main(null);
Init method = Recursion
fibonacci Number 20 = 4181
fibonacci List = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765]
fibonacci Hashmap = {0=[0], 1=[0, 1], 2=[0, 1, 1], 3=[0, 1, 1, 2], 4=[0, 1, 1, 2, 3], 5=[0, 1, 1, 2, 3, 5], 6=[0, 1, 1, 2, 3, 5, 8], 7=[0, 1, 1, 2, 3, 5, 8, 13], 8=[0, 1, 1, 2, 3, 5, 8, 13, 21], 9=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34], 10=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55], 11=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89], 12=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144], 13=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233], 14=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377], 15=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610], 16=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987], 17=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597], 18=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584], 19=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181], 20=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765]}
fibonacci Sequence 1 = [0]
fibonacci Sequence 2 = [0, 1]
fibonacci Sequence 3 = [0, 1, 1]
fibonacci Sequence 4 = [0, 1, 1, 2]
fibonacci Sequence 5 = [0, 1, 1, 2, 3]
fibonacci Sequence 6 = [0, 1, 1, 2, 3, 5]
fibonacci Sequence 7 = [0, 1, 1, 2, 3, 5, 8]
fibonacci Sequence 8 = [0, 1, 1, 2, 3, 5, 8, 13]
fibonacci Sequence 9 = [0, 1, 1, 2, 3, 5, 8, 13, 21]
fibonacci Sequence 10 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
fibonacci Sequence 11 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
fibonacci Sequence 12 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
fibonacci Sequence 13 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
fibonacci Sequence 14 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233]
fibonacci Sequence 15 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]
fibonacci Sequence 16 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]
fibonacci Sequence 17 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]
fibonacci Sequence 18 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597]
fibonacci Sequence 19 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584]
fibonacci Sequence 20 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]

Recursion Example:

public static long fib(long n) { if ((n == 0) || (n == 1)) return n; else return fib(n - 1) + fib(n - 2); }

The method fib() calculates the fibonacci number at position n. If n is equal to 0 or 1, it returns n. Otherwise it recursively calls itself and returns fib(n - 1) + fib(n - 2).

  • public static int fib(int i) { if ((i == 0) || (i == 1)) {
    return i;
    
    } else{ return fib(i - 1) + fib(i - 2); } }