Tribonacci Word

• Difficulty Level : Basic
• Last Updated : 30 Apr, 2021

Like Fibonacci word, a Tribonacci word. is a specific sequence of digits. The Tribonacci word is formed by repeated concatenation in the same way that the Fibonacci word is formed by repeated addition. But unlike the fibonacci word, Tribonacci word is formed by repeated addition of last three terms and it has its first three terms different from each other.

```In Tribonacci word,
S(0) = 1,
S(1) = 12,
S(2) = 1213,
S(3) = 1213121
.....
where S(n) = S(n-1) + S(n-2) + S(n-3) and +
represents the concatenation of
strings. ```

The task is to find nth Tribonacci word for a given number n.
Examples:

```Input : n = 4
Output : S(4) = 1213121121312

Input : n = 3
Output : S(3) = 1213121```

Just like in program of Fibonacci word, we use the iterative concept of finding nth Fibonacci word here for finding nth Tribonacci word we can use the iterative concept. So for finding nth Tribonacci word we will take three string Sn_1, Sn_2 and Sn_3 which represent S(n-1), S(n-2) and S(n-3) respectively and on each iteration we will update tmp = Sn_3, Sn_3 = Sn_3 + Sn_2 + Sn_1, Sn_1 = Sn_2 and Sn_2 = tmp in this way we can find nth tribonacci word.

C++

 `// C++ program for nth Fibonacci word``#include ``using` `namespace` `std;` `// Returns n-th Tribonacci word``string tribWord(``int` `n) {``  ``string Sn_1 = ``"1"``;``  ``string Sn_2 = ``"12"``;``  ``string Sn_3 = ``"1213"``;``  ``string tmp;``  ``for` `(``int` `i = 3; i <= n; i++) {``    ``tmp = Sn_3;``    ``Sn_3 += (Sn_2 + Sn_1);``    ``Sn_1 = Sn_2;``    ``Sn_2 = tmp;``  ``}` `  ``return` `Sn_3;``}` `// driver program``int` `main() {``  ``int` `n = 6;``  ``cout << tribWord(n);``  ``return` `0;``}`

Java

 `// program for nth Tribonacci word``class` `GFG {` `// Returns n-th Tribonacci word``static` `String tribWord(``int` `n) {``    ``String Sn_1 = ``"1"``;``    ``String Sn_2 = ``"12"``;``    ``String Sn_3 = ``"1213"``;``    ``String tmp;``    ``for` `(``int` `i = ``3``; i <= n; i++) {``    ``tmp = Sn_3;``    ``Sn_3 += (Sn_2 + Sn_1);``    ``Sn_1 = Sn_2;``    ``Sn_2 = tmp;``    ``}` `    ``return` `Sn_3;``}` `// Driver code``public` `static` `void` `main(String[] args) {``    ``int` `n = ``6``;``    ``System.out.print(tribWord(n));``}``}``// This code is contributed by Anant Agarwal.`

Python3

 `# Python3 Program for nth``# Tribonacci word` `# Returns n-th Tribonacci word``def` `tribWord(n):``    ``Sn_1 ``=` `"1"``    ``Sn_2 ``=` `"12"``    ``Sn_3 ``=` `"1213"``    ``for` `i ``in` `range``(``3``, n``+``1``):``        ``tmp ``=` `Sn_3``        ``Sn_3 ``+``=` `(Sn_2 ``+` `Sn_1)``        ``Sn_1 ``=` `Sn_2``        ``Sn_2 ``=` `tmp` `    ``return` `Sn_3` `# Driver code``n ``=` `6``print``(tribWord(n))` `# This code is contributed By Anant Agarwal.`

C#

 `// C# program for nth Tribonacci word``using` `System;` `class` `GFG {` `    ``// Returns n-th Tribonacci word``    ``static` `string` `tribWord(``int` `n)``    ``{``        ``string` `Sn_1 = ``"1"``;``        ``string` `Sn_2 = ``"12"``;``        ``string` `Sn_3 = ``"1213"``;``        ``string` `tmp;``        ` `        ``for` `(``int` `i = 3; i <= n; i++) {``            ``tmp = Sn_3;``            ``Sn_3 += (Sn_2 + Sn_1);``            ``Sn_1 = Sn_2;``            ``Sn_2 = tmp;``        ``}``    ` `        ``return` `Sn_3;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main() {``        ` `        ``int` `n = 6;``        ` `        ``Console.WriteLine(tribWord(n));``    ``}``}` `// This code is contributed by vt_m.`

PHP

 ``

Javascript

 ``

Output:

`12131211213121213121121312131211213121213121`

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