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
Try It Yourself
A simple solution is to simply follow recursive formula and write recursive code for it,
// 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;
}
// 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.
# 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.
<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
// 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:
// 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;
}
// 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
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
// 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:
// 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;
}
// 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.*/
# 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.*/
<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
// 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.
// 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;
}
// 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.
# 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.
<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
// 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.
#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 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.
# 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.
<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
// 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