Tribonacci Series in Java

The Tribonacci series is similar to the Fibonacci series. The Tribonacci sequence is a generalization of the Fibonacci sequence where each term is the sum of the three preceding terms.

Tribonacci Series

A Tribonacci sequence or series is a sequence of integers such that each term from the fourth onward is the sum of the previous three terms. The Tribonacci sequence can be defined as follows:

T₀=0,
T₁=T₂=1
T_n=T_n-1+T_n-2+T_n-3(n≥3)

In other words, we can say that each term of the series is the sum of the previous three terms. The first few terms of Tribonacci series are:

0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591, 29249425, 53798080, 98950096, 181997601, 334745777, 615693474, 1132436852… so on.

Tribonacci Series Java Program

In the Tribonacci sequence, the first three terms are initialized. From the fourth and onwards, we sum up the last three terms to get the next term.

Let's implement the logic in a Java program.

TribonacciSeries.java

import java.util.*;
public class TribonacciSeries
{
public static void main(String args[])
{
Scanner sc = new Scanner(System.in);
System.out.print("Enter No. of terms: ");
int n=sc.nextInt();
int a = 1, b = 0, c = 1;
int d = a + b + c;
System.out.println("\nTribonacci Series: ");
System.out.print(a+"\t"+b+"\t"+c);
for(int i=4; i<=n; i++)
{
System.out.print("\t"+d);
a=b;
b=c;
c=d;
d=a+b+c;
}
System.out.println();
}
}

Output:

Enter No. of terms: 15
Tribonacci Series is given below: 
0	1	1	2	4	7	13	24	44	81	149	274	504 927	1705

Find N^th Term of the Tribonacci Series

NthTribonacciTerm.java

import java.util.*; 
public class NthTribonacciTerm
{
//method to calculate Tribonnaci series 
public static int tribonacciTerm(int n) 
{
if (n < 3) 
return n;
//initializing the first three terms of the Tribonnaci series
int a = 0, b = 1, c = 1, d;
//in the while loop --> is not an operator. These are two separate operators, -- and >.
//the conditional's code decrements n by 1, while returning n's original value not decremented value
//after that compares the original value with 3 using the > operator.
//more specifically we can write it as while ((n--) > 3)   
while (n-- > 3)   
{
d = a + b + c;
a = b;
b = c;
c = d;
}
return c;
}
public static void main(String args[]) 
{
Scanner sc = new Scanner(System.in);
System.out.print("Enter the term: ");
//reads an integer from the user 
int n=sc.nextInt();
//function calling
int ans=tribonacciTerm(n); 
System.out.println("The "+n+"th term of the Tribonacci series is: "+ans);
}
}

Output:

Enter the term: 15
The 15th term of the Tribonacci series is: 1705

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Tribonacci Series in Java