Tribonacci Numbers

Last Updated : 13 Nov, 2024

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

a(n) = a(n-1) + a(n-2) + a(n-3)
with
a(0) = a(1) = 0, a(2) = 1.

First few numbers in the Tribonacci Sequence are 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, ….

Given a value n, task is to print first n Tribonacci Numbers.
Examples:

Input : 5
Output : 0, 0, 1, 1, 2

Input : 10
Output : 0, 0, 1, 1, 2, 4, 7, 13, 24, 44

Input : 20
Output : 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513

A simple solution is to simply follow recursive formula and write recursive code for it,

C++

// A simple recursive CPP program to print // first n Tribonacci numbers. #include <iostream> using namespace std;  int printTribRec(int n) {     if (n == 0 || n == 1 || n == 2)         return 0;      if (n == 3)         return 1;     else         return printTribRec(n - 1) +                 printTribRec(n - 2) +                 printTribRec(n - 3); }  void printTrib(int n) {     for (int i = 1; i < n; i++)         cout << printTribRec(i) << " "; }  // Driver code int main() {     int n = 10;     printTrib(n);     return 0; }

Java

// A simple recursive CPP program // first n Tribonacci numbers. import java.io.*;  class GFG {          // Recursion Function     static int printTribRec(int n)     {                  if (n == 0 || n == 1 || n == 2)             return 0;                      if (n == 3)             return 1;         else             return printTribRec(n - 1) +                     printTribRec(n - 2) +                    printTribRec(n - 3);     }          static void printTrib(int n)     {         for (int i = 1; i < n; i++)             System.out.print(printTribRec(i)                              +" ");     }           // Driver code     public static void main(String args[])     {         int n = 10;          printTrib(n);     } }  // This code is contributed by Nikita tiwari.

Python

# A simple recursive CPP program to print # first n Tribonacci numbers.  def printTribRec(n) :     if (n == 0 or n == 1 or n == 2) :         return 0     elif (n == 3) :         return 1     else :         return (printTribRec(n - 1) +                  printTribRec(n - 2) +                 printTribRec(n - 3))           def printTrib(n) :     for i in range(1, n) :         print( printTribRec(i) , " ", end = "")           # Driver code n = 10 printTrib(n)   # This code is contributed by Nikita Tiwari.

// A simple recursive C# program // first n Tribinocci numbers. using System;  class GFG {          // Recursion Function     static int printTribRec(int n)     {                  if (n == 0 || n == 1 || n == 2)             return 0;                      if (n == 3)             return 1;         else             return printTribRec(n - 1) +                     printTribRec(n - 2) +                    printTribRec(n - 3);     }          static void printTrib(int n)     {         for (int i = 1; i < n; i++)             Console.Write(printTribRec(i)                                     +" ");     }          // Driver code     public static void Main()     {         int n = 10;          printTrib(n);     } }  // This code is contributed by vt_m.

JavaScript

<script> // A simple recursive Javascript program to // print first n Tribinocci numbers.  function printTribRec(n) {     if (n == 0 || n == 1 || n == 2)         return 0;      if (n == 3)         return 1;     else         return printTribRec(n - 1) +             printTribRec(n - 2) +             printTribRec(n - 3); }  function printTrib(n) {     for (let i = 1; i <= n; i++)         document.write(printTribRec(i) + " "); }      // Driver Code     let n = 10;     printTrib(n);  // This code is contributed by _saurabh_jaiswal </script>

PHP

<?php // A simple recursive PHP program to  // print first n Tribinocci numbers.  function printTribRec($n) {     if ($n == 0 || $n == 1 || $n == 2)         return 0;      if ($n == 3)         return 1;     else         return printTribRec($n - 1) +                 printTribRec($n - 2) +                 printTribRec($n - 3); }  function printTrib($n) {     for ($i = 1; $i <= $n; $i++)         echo printTribRec($i), " "; }      // Driver Code     $n = 10;     printTrib($n);  // This code is contributed by ajit ?>

Output

0 0 1 1 2 4 7 13 24

Time complexity of above solution is exponential.
A better solution is to use Dynamic Programming.

1) Top-Down Dp Memoization:

C++

// A simple recursive CPP program to print // first n Tribonacci numbers. #include <bits/stdc++.h> using namespace std;  int printTribRec(int n, vector<int> &dp) {     if (n == 0 || n == 1 || n == 2)         return 0;        if(dp[n] != -1){         return dp[n] ;     }      if (n == 3)         return 1;     else         return dp[n] = printTribRec(n - 1, dp) +                         printTribRec(n - 2, dp) +                         printTribRec(n - 3, dp); }  void printTrib(int n) {     // dp vector to store subproblems     vector<int> dp(n+1, -1) ;     for (int i = 1; i < n; i++)         cout << printTribRec(i, dp) << " "; }  // Driver code int main() {     int n = 10;     printTrib(n);     return 0; }

Java

// A simple recursive Java program to print // first n Tribonacci numbers.  import java.util.*;   class GFG {     static int printTribRec(int n, int[] dp)     {         if (n == 0 || n == 1 || n == 2)             return 0;          if (dp[n] != -1) {             return dp[n];         }          if (n == 3)             return 1;         else             return dp[n] = printTribRec(n - 1, dp)                            + printTribRec(n - 2, dp)                            + printTribRec(n - 3, dp);     }      static void printTrib(int n)     {         // dp vector to store subproblems         int[] dp = new int[n + 1];         for (var i = 0; i <= n; i++)             dp[i] = -1;         for (int i = 1; i < n; i++)             System.out.print(printTribRec(i, dp) + " ");     }      // Driver code     public static void main(String[] args)     {         int n = 10;         printTrib(n);     } }  // This code is contributed by phasing17

Python

def tribonacci(n):      h={} #creating the dictionary to store the results     def tribo(n):         if n in h:             return h[n]         if n==0:             return 0         elif n==1 or n==2:             return 1         else:             res=tribo(n-3)+tribo(n-2)+tribo(n-1)             h[n]=res #storing the results so that we can reuse it again          return res     return tribo(n) n=10 for i in range(n):     print(tribonacci(i),end=' ')

// A simple recursive C# program to print // first n Tribonacci numbers.  using System; using System.Collections.Generic;  class GFG {     static int printTribRec(int n, List<int> dp)     {         if (n == 0 || n == 1 || n == 2)             return 0;          if (dp[n] != -1) {             return dp[n];         }          if (n == 3)             return 1;         else             return dp[n] = printTribRec(n - 1, dp)                            + printTribRec(n - 2, dp)                            + printTribRec(n - 3, dp);     }      static void printTrib(int n)     {         // dp vector to store subproblems         List<int> dp = new List<int>();         for (var i = 0; i <= n; i++)             dp.Add(-1);         for (int i = 1; i < n; i++)             Console.Write(printTribRec(i, dp) + " ");     }      // Driver code     public static void Main(string[] args)     {         int n = 10;         printTrib(n);     } }  // This code is contributed by phasing17

JavaScript

// A simple recursive JS program to print // first n Tribonacci numbers.  function printTribRec(n, dp) {     if (n == 0 || n == 1 || n == 2)         return 0;        if(dp[n] != -1){         return dp[n] ;     }      if (n == 3)         return 1;     else         return dp[n] = printTribRec(n - 1, dp) +                         printTribRec(n - 2, dp) +                         printTribRec(n - 3, dp); }  function printTrib(n) {     // dp vector to store subproblems     let dp = new Array(n+1).fill(-1) ;     for (var i = 1; i < n; i++)         process.stdout.write(printTribRec(i, dp) + " "); }  // Driver code let n = 10; printTrib(n);   // This code is contributed by phasing17

Output

0 0 1 1 2 4 7 13 24

2) Bottom-Up DP Tabulation:

C++

// A DP based CPP // program to print // first n Tribonacci // numbers. #include <iostream> using namespace std;  int printTrib(int n) {     int dp[n];     dp[0] = dp[1] = 0;     dp[2] = 1;      for (int i = 3; i < n; i++)         dp[i] = dp[i - 1] +                  dp[i - 2] +                 dp[i - 3];      for (int i = 0; i < n; i++)         cout << dp[i] << " "; }  // Driver code int main() {     int n = 10;     printTrib(n);     return 0; }

Java

// A DP based Java program // to print first n // Tribonacci numbers. import java.io.*;  class GFG {          static void printTrib(int n)     {         int dp[]=new int[n];         dp[0] = dp[1] = 0;         dp[2] = 1;              for (int i = 3; i < n; i++)             dp[i] = dp[i - 1] +                     dp[i - 2] +                     dp[i - 3];              for (int i = 0; i < n; i++)             System.out.print(dp[i] + " ");     }          // Driver code     public static void main(String args[])     {         int n = 10;         printTrib(n);     } }  /* This code is contributed by Nikita Tiwari.*/

Python

# A DP based # Python 3  # program to print # first n Tribonacci # numbers.  def printTrib(n) :      dp = [0] * n     dp[0] = dp[1] = 0;     dp[2] = 1;      for i in range(3,n) :         dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3];      for i in range(0,n) :         print(dp[i] , " ", end="")           # Driver code n = 10 printTrib(n)  # This code is contributed by Nikita Tiwari.

// A DP based C# program // to print first n // Tribonacci numbers. using System;  class GFG {          static void printTrib(int n)     {         int []dp = new int[n];         dp[0] = dp[1] = 0;         dp[2] = 1;              for (int i = 3; i < n; i++)             dp[i] = dp[i - 1] +                     dp[i - 2] +                     dp[i - 3];              for (int i = 0; i < n; i++)         Console.Write(dp[i] + " ");     }          // Driver code     public static void Main()     {         int n = 10;         printTrib(n);     } }  /* This code is contributed by vt_m.*/

JavaScript

<script> // Javascript program // to print first n // Tribonacci numbers.     function printTrib(n)     {         let dp = Array.from({length: n}, (_, i) => 0);         dp[0] = dp[1] = 0;         dp[2] = 1;               for (let i = 3; i < n; i++)             dp[i] = dp[i - 1] +                     dp[i - 2] +                     dp[i - 3];               for (let i = 0; i < n; i++)             document.write(dp[i] + " ");     }    // driver function         let n = 10;         printTrib(n);      // This code is contributed by code_hunt. </script>

PHP

<?php // A DP based PHP program  // to print first n  // Tribonacci numbers.  function printTrib($n) {      $dp[0] = $dp[1] = 0;     $dp[2] = 1;      for ($i = 3; $i < $n; $i++)         $dp[$i] = $dp[$i - 1] +                    $dp[$i - 2] +                   $dp[$i - 3];      for ($i = 0; $i < $n; $i++)         echo $dp[$i] ," "; }  // Driver code $n = 10; printTrib($n);  // This code is contributed by ajit ?>

Output

0 0 1 1 2 4 7 13 24 44

Time complexity of above is linear, but it requires extra space. We can optimizes space used in above solution using three variables to keep track of previous three numbers.

C++

// A space optimized // based CPP program to // print first n // Tribonacci numbers. #include <iostream> using namespace std;  void printTrib(int n) {     if (n < 1)         return;      // Initialize first     // three numbers     int first = 0, second = 0;     int third = 1;      cout << first << " ";     if (n > 1)         cout << second << " ";          if (n > 2)         cout << second << " ";      // Loop to add previous      // three numbers for     // each number starting      // from 3 and then assign     // first, second, third     // to second, third, and      // curr to third respectively     for (int i = 3; i < n; i++)      {         int curr = first + second + third;         first = second;         second = third;         third = curr;          cout << curr << " ";     } }  // Driver code int main() {     int n = 10;     printTrib(n);     return 0; }

Java

// A space optimized // based Java program // to print first n  // Tribinocci numbers. import java.io.*;  class GFG {          static void printTrib(int n)     {         if (n < 1)             return;              // Initialize first         // three numbers         int first = 0, second = 0;         int third = 1;              System.out.print(first + " ");         if (n > 1)             System.out.print(second + " ");                  if (n > 2)             System.out.print(second + " ");              // Loop to add previous         // three numbers for         // each number starting         // from 3 and then assign         // first, second, third         // to second, third, and curr         // to third respectively         for (int i = 3; i < n; i++)          {             int curr = first + second + third;             first = second;             second = third;             third = curr;                  System.out.print(curr +" ");         }     }          // Driver code     public static void main(String args[])     {         int n = 10;         printTrib(n);     } }  // This code is contributed by Nikita Tiwari.

Python

# A space optimized # based Python 3  # program to print # first n Tribinocci  # numbers.  def printTrib(n) :     if (n < 1) :         return       # Initialize first     # three numbers     first = 0     second = 0     third = 1      print( first , " ", end="")     if (n > 1) :         print(second, " ",end="")     if (n > 2) :         print(second, " ", end="")      # Loop to add previous     # three numbers for     # each number starting     # from 3 and then assign     # first, second, third     # to second, third, and curr     # to third respectively     for i in range(3, n) :         curr = first + second + third         first = second         second = third         third = curr          print(curr , " ", end="")           # Driver code n = 10 printTrib(n)  # This code is contributed by Nikita Tiwari.

// A space optimized // based C# program // to print first n  // Tribinocci numbers. using System;  class GFG {          static void printTrib(int n)     {         if (n < 1)             return;              // Initialize first         // three numbers         int first = 0, second = 0;         int third = 1;              Console.Write(first + " ");         if (n > 1)         Console.Write(second + " ");                  if (n > 2)         Console.Write(second + " ");              // Loop to add previous         // three numbers for         // each number starting         // from 3 and then assign         // first, second, third         // to second, third, and curr         // to third respectively         for (int i = 3; i < n; i++)          {             int curr = first + second + third;             first = second;             second = third;             third = curr;                  Console.Write(curr +" ");         }     }          // Driver code     public static void Main()     {         int n = 10;         printTrib(n);     } }  // This code is contributed by vt_m.

JavaScript

<script>  // A space optimized // based Javascript program // to print first n // Tribonacci numbers.          function printTrib(n)     {         if (n < 1)             return;               // Initialize first         // three numbers         let first = 0, second = 0;         let third = 1;               document.write(first + " ");         if (n > 1)             document.write(second + " ");                   if (n > 2)             document.write(second + " ");               // Loop to add previous         // three numbers for         // each number starting         // from 3 and then assign         // first, second, third         // to second, third, and curr         // to third respectively         for (let i = 3; i < n; i++)         {             let curr = first + second + third;             first = second;             second = third;             third = curr;                   document.write(curr +" ");         }     }          // Driver code     let n = 10;     printTrib(n);          // This code is contributed by rag2127      </script>

PHP

<?php // A space optimized // based PHP program to // print first n // Tribinocci numbers.|  function printTrib($n) {     if ($n < 1)         return;      // Initialize first     // three numbers     $first = 0; $second = 0;     $third = 1;      echo $first, " ";     if ($n > 1)         echo $second , " ";          if ($n > 2)         echo $second , " ";      // Loop to add previous      // three numbers for     // each number starting      // from 3 and then assign     // first, second, third     // to second, third, and      // curr to third respectively     for ($i = 3; $i < $n; $i++)      {         $curr = $first + $second + $third;         $first = $second;         $second = $third;         $third = $curr;          echo $curr , " ";     } }      // Driver code     $n = 10;     printTrib($n);  // This code is contributed by m_kit ?>

Output

0 0 0 1 2 4 7 13 24 44

Below is more efficient solution using matrix exponentiation.

C++

#include <iostream> using namespace std;  // Program to print first n  // tribonacci numbers Matrix  // Multiplication function  // for 3*3 matrix void multiply(int T[3][3], int M[3][3]) {     int a, b, c, d, e, f, g, h, i;     a = T[0][0] * M[0][0] +          T[0][1] * M[1][0] +          T[0][2] * M[2][0];     b = T[0][0] * M[0][1] +          T[0][1] * M[1][1] +          T[0][2] * M[2][1];     c = T[0][0] * M[0][2] +          T[0][1] * M[1][2] +          T[0][2] * M[2][2];     d = T[1][0] * M[0][0] +          T[1][1] * M[1][0] +          T[1][2] * M[2][0];     e = T[1][0] * M[0][1] +          T[1][1] * M[1][1] +          T[1][2] * M[2][1];     f = T[1][0] * M[0][2] +          T[1][1] * M[1][2] +          T[1][2] * M[2][2];     g = T[2][0] * M[0][0] +          T[2][1] * M[1][0] +          T[2][2] * M[2][0];     h = T[2][0] * M[0][1] +          T[2][1] * M[1][1] +          T[2][2] * M[2][1];     i = T[2][0] * M[0][2] +          T[2][1] * M[1][2] +          T[2][2] * M[2][2];     T[0][0] = a;     T[0][1] = b;     T[0][2] = c;     T[1][0] = d;     T[1][1] = e;     T[1][2] = f;     T[2][0] = g;     T[2][1] = h;     T[2][2] = i; }  // Recursive function to raise  // the matrix T to the power n void power(int T[3][3], int n) {     // base condition.     if (n == 0 || n == 1)         return;     int M[3][3] = {{ 1, 1, 1 },                     { 1, 0, 0 },                     { 0, 1, 0 }};      // recursively call to     // square the matrix     power(T, n / 2);      // calculating square      // of the matrix T     multiply(T, T);      // if n is odd multiply      // it one time with M     if (n % 2)         multiply(T, M); } int tribonacci(int n) {     int T[3][3] = {{ 1, 1, 1 },                     { 1, 0, 0 },                    { 0, 1, 0 }};      // base condition     if (n == 0 || n == 1)         return 0;     else         power(T, n - 2);      // T[0][0] contains the      // tribonacci number so     // return it     return T[0][0]; }  // Driver Code int main() {     int n = 10;     for (int i = 0; i < n; i++)         cout << tribonacci(i) << " ";     cout << endl;     return 0; }

Java

// Java Program to print // first n tribonacci numbers // Matrix Multiplication // function for 3*3 matrix import java.io.*;  class GFG  {     static void multiply(int T[][], int M[][])     {         int a, b, c, d, e, f, g, h, i;         a = T[0][0] * M[0][0] +              T[0][1] * M[1][0] +              T[0][2] * M[2][0];         b = T[0][0] * M[0][1] +              T[0][1] * M[1][1] +              T[0][2] * M[2][1];         c = T[0][0] * M[0][2] +              T[0][1] * M[1][2] +              T[0][2] * M[2][2];         d = T[1][0] * M[0][0] +              T[1][1] * M[1][0] +              T[1][2] * M[2][0];         e = T[1][0] * M[0][1] +              T[1][1] * M[1][1] +              T[1][2] * M[2][1];         f = T[1][0] * M[0][2] +              T[1][1] * M[1][2] +              T[1][2] * M[2][2];         g = T[2][0] * M[0][0] +              T[2][1] * M[1][0] +              T[2][2] * M[2][0];         h = T[2][0] * M[0][1] +              T[2][1] * M[1][1] +              T[2][2] * M[2][1];         i = T[2][0] * M[0][2] +              T[2][1] * M[1][2] +              T[2][2] * M[2][2];         T[0][0] = a;         T[0][1] = b;         T[0][2] = c;         T[1][0] = d;         T[1][1] = e;         T[1][2] = f;         T[2][0] = g;         T[2][1] = h;         T[2][2] = i;     }          // Recursive function to raise      // the matrix T to the power n     static void power(int T[][], int n)     {         // base condition.         if (n == 0 || n == 1)             return;         int M[][] = {{ 1, 1, 1 },                       { 1, 0, 0 },                       { 0, 1, 0 }};              // recursively call to          // square the matrix         power(T, n / 2);              // calculating square          // of the matrix T         multiply(T, T);              // if n is odd multiply         // it one time with M         if (n % 2 != 0)             multiply(T, M);     }     static int tribonacci(int n)     {         int T[][] = {{ 1, 1, 1 },                       { 1, 0, 0 },                      { 0, 1, 0 }};              // base condition         if (n == 0 || n == 1)             return 0;         else             power(T, n - 2);              // T[0][0] contains the          // tribonacci number so         // return it         return T[0][0];     }          // Driver Code     public static void main(String args[])     {         int n = 10;         for (int i = 0; i < n; i++)         System.out.print(tribonacci(i) + " ");         System.out.println();     } }  // This code is contributed by Nikita Tiwari.

Python

# Program to print first n tribonacci  # numbers Matrix Multiplication # function for 3*3 matrix def multiply(T, M):          a = (T[0][0] * M[0][0] + T[0][1] *          M[1][0] + T[0][2] * M[2][0])                  b = (T[0][0] * M[0][1] + T[0][1] *           M[1][1] + T[0][2] * M[2][1])      c = (T[0][0] * M[0][2] + T[0][1] *           M[1][2] + T[0][2] * M[2][2])     d = (T[1][0] * M[0][0] + T[1][1] *           M[1][0] + T[1][2] * M[2][0])      e = (T[1][0] * M[0][1] + T[1][1] *           M[1][1] + T[1][2] * M[2][1])     f = (T[1][0] * M[0][2] + T[1][1] *          M[1][2] + T[1][2] * M[2][2])     g = (T[2][0] * M[0][0] + T[2][1] *           M[1][0] + T[2][2] * M[2][0])     h = (T[2][0] * M[0][1] + T[2][1] *           M[1][1] + T[2][2] * M[2][1])     i = (T[2][0] * M[0][2] + T[2][1] *           M[1][2] + T[2][2] * M[2][2])                  T[0][0] = a     T[0][1] = b     T[0][2] = c     T[1][0] = d     T[1][1] = e     T[1][2] = f     T[2][0] = g     T[2][1] = h     T[2][2] = i  # Recursive function to raise  # the matrix T to the power n def power(T, n):      # base condition.     if (n == 0 or n == 1):         return;     M = [[ 1, 1, 1 ],                  [ 1, 0, 0 ],                  [ 0, 1, 0 ]]      # recursively call to     # square the matrix     power(T, n // 2)      # calculating square      # of the matrix T     multiply(T, T)      # if n is odd multiply      # it one time with M     if (n % 2):         multiply(T, M)  def tribonacci(n):          T = [[ 1, 1, 1 ],          [1, 0, 0 ],         [0, 1, 0 ]]      # base condition     if (n == 0 or n == 1):         return 0     else:         power(T, n - 2)      # T[0][0] contains the      # tribonacci number so     # return it     return T[0][0]  # Driver Code if __name__ == "__main__":     n = 10     for i in range(n):         print(tribonacci(i),end=" ")     print()  # This code is contributed by ChitraNayal

// C# Program to print // first n tribonacci numbers // Matrix Multiplication // function for 3*3 matrix using System;  class GFG  {     static void multiply(int [,]T,                           int [,]M)     {         int a, b, c, d, e, f, g, h, i;         a = T[0,0] * M[0,0] +              T[0,1] * M[1,0] +              T[0,2] * M[2,0];         b = T[0,0] * M[0,1] +              T[0,1] * M[1,1] +              T[0,2] * M[2,1];         c = T[0,0] * M[0,2] +              T[0,1] * M[1,2] +              T[0,2] * M[2,2];         d = T[1,0] * M[0,0] +              T[1,1] * M[1,0] +              T[1,2] * M[2,0];         e = T[1,0] * M[0,1] +              T[1,1] * M[1,1] +              T[1,2] * M[2,1];         f = T[1,0] * M[0,2] +              T[1,1] * M[1,2] +              T[1,2] * M[2,2];         g = T[2,0] * M[0,0] +              T[2,1] * M[1,0] +              T[2,2] * M[2,0];         h = T[2,0] * M[0,1] +              T[2,1] * M[1,1] +              T[2,2] * M[2,1];         i = T[2,0] * M[0,2] +              T[2,1] * M[1,2] +              T[2,2] * M[2,2];         T[0,0] = a;         T[0,1] = b;         T[0,2] = c;         T[1,0] = d;         T[1,1] = e;         T[1,2] = f;         T[2,0] = g;         T[2,1] = h;         T[2,2] = i;     }          // Recursive function to raise      // the matrix T to the power n     static void power(int [,]T, int n)     {         // base condition.         if (n == 0 || n == 1)             return;         int [,]M = {{ 1, 1, 1 },                      { 1, 0, 0 },                      { 0, 1, 0 }};              // recursively call to          // square the matrix         power(T, n / 2);              // calculating square          // of the matrix T         multiply(T, T);              // if n is odd multiply          // it one time with M         if (n % 2 != 0)             multiply(T, M);     }          static int tribonacci(int n)     {         int [,]T = {{ 1, 1, 1 },                      { 1, 0, 0 },                     { 0, 1, 0 }};              // base condition         if (n == 0 || n == 1)             return 0;         else             power(T, n - 2);              // T[0][0] contains the          // tribonacci number so         // return it         return T[0,0];     }          // Driver Code     public static void Main()     {         int n = 10;         for (int i = 0; i < n; i++)         Console.Write(tribonacci(i) + " ");         Console.WriteLine();     } }  // This code is contributed by vt_m.

JavaScript

<script>  // javascript Program to print // first n tribonacci numbers // Matrix Multiplication // function for 3*3 matrix      function multiply(T , M)     {         var a, b, c, d, e, f, g, h, i;         a = T[0][0] * M[0][0] +              T[0][1] * M[1][0] +              T[0][2] * M[2][0];         b = T[0][0] * M[0][1] +              T[0][1] * M[1][1] +              T[0][2] * M[2][1];         c = T[0][0] * M[0][2] +              T[0][1] * M[1][2] +              T[0][2] * M[2][2];         d = T[1][0] * M[0][0] +              T[1][1] * M[1][0] +              T[1][2] * M[2][0];         e = T[1][0] * M[0][1] +              T[1][1] * M[1][1] +              T[1][2] * M[2][1];         f = T[1][0] * M[0][2] +              T[1][1] * M[1][2] +              T[1][2] * M[2][2];         g = T[2][0] * M[0][0] +              T[2][1] * M[1][0] +              T[2][2] * M[2][0];         h = T[2][0] * M[0][1] +              T[2][1] * M[1][1] +              T[2][2] * M[2][1];         i = T[2][0] * M[0][2] +              T[2][1] * M[1][2] +              T[2][2] * M[2][2];         T[0][0] = a;         T[0][1] = b;         T[0][2] = c;         T[1][0] = d;         T[1][1] = e;         T[1][2] = f;         T[2][0] = g;         T[2][1] = h;         T[2][2] = i;     }          // Recursive function to raise      // the matrix T to the power n     function power(T , n)     {         // base condition.         if (n == 0 || n == 1)             return;         var M = [[ 1, 1, 1 ],                       [ 1, 0, 0 ],                       [ 0, 1, 0 ]];              // recursively call to          // square the matrix         power(T, parseInt(n / 2));              // calculating square          // of the matrix T         multiply(T, T);              // if n is odd multiply         // it one time with M         if (n % 2 != 0)             multiply(T, M);     }     function tribonacci(n)     {         var T = [[ 1, 1, 1 ],                       [ 1, 0, 0 ],                      [ 0, 1, 0 ]];              // base condition         if (n == 0 || n == 1)             return 0;         else             power(T, n - 2);              // T[0][0] contains the          // tribonacci number so         // return it         return T[0][0];     }          // Driver Code     var n = 10;     for (var i = 0; i < n; i++)     document.write(tribonacci(i) + " ");     document.write('<br>');   // This code contributed by shikhasingrajput  </script>

PHP

 <?php // Program to print first n tribonacci numbers  // Matrix Multiplication function for 3*3 matrix function multiply(&$T, $M) {     $a = $T[0][0] * $M[0][0] +           $T[0][1] * $M[1][0] +           $T[0][2] * $M[2][0];     $b = $T[0][0] * $M[0][1] +           $T[0][1] * $M[1][1] +           $T[0][2] * $M[2][1];     $c = $T[0][0] * $M[0][2] +           $T[0][1] * $M[1][2] +           $T[0][2] * $M[2][2];     $d = $T[1][0] * $M[0][0] +           $T[1][1] * $M[1][0] +           $T[1][2] * $M[2][0];     $e = $T[1][0] * $M[0][1] +           $T[1][1] * $M[1][1] +           $T[1][2] * $M[2][1];     $f = $T[1][0] * $M[0][2] +           $T[1][1] * $M[1][2] +           $T[1][2] * $M[2][2];     $g = $T[2][0] * $M[0][0] +           $T[2][1] * $M[1][0] +           $T[2][2] * $M[2][0];     $h = $T[2][0] * $M[0][1] +           $T[2][1] * $M[1][1] +           $T[2][2] * $M[2][1];     $i = $T[2][0] * $M[0][2] +           $T[2][1] * $M[1][2] +           $T[2][2] * $M[2][2];     $T[0][0] = $a;     $T[0][1] = $b;     $T[0][2] = $c;     $T[1][0] = $d;     $T[1][1] = $e;     $T[1][2] = $f;     $T[2][0] = $g;     $T[2][1] = $h;     $T[2][2] = $i; }  // Recursive function to raise  // the matrix T to the power n function power(&$T,$n) {     // base condition.     if ($n == 0 || $n == 1)         return;     $M = array(array( 1, 1, 1 ),                 array( 1, 0, 0 ),                 array( 0, 1, 0 ));      // recursively call to     // square the matrix     power($T, (int)($n / 2));      // calculating square      // of the matrix T     multiply($T, $T);      // if n is odd multiply      // it one time with M     if ($n % 2)         multiply($T, $M); }  function tribonacci($n) {     $T = array(array( 1, 1, 1 ),                 array( 1, 0, 0 ),                array( 0, 1, 0 ));      // base condition     if ($n == 0 || $n == 1)         return 0;     else         power($T, $n - 2);      // $T[0][0] contains the tribonacci      // number so return it     return $T[0][0]; }  // Driver Code $n = 10; for ($i = 0; $i < $n; $i++)     echo tribonacci($i) . " "; echo "\n";  // This code is contributed by mits ?>

Output

0 0 1 1 2 4 7 13 24 44

Geek-onacci Number

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Tribonacci Numbers

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