# Program to print Fibonacci Triangle

Given the value of n(n < 10), i.e, number of lines, print the Fibonacci triangle.
Examples:

```Input : n = 5
Output :
1
1 2
3 5 8
13 21 34 55
89 144 233 377 610

Input : n = 7
Output :
1
1 2
3 5 8
13 21 34 55
89 144 233 377 610
987 1597 2584 4181 6765 10946
17711 28657 46368 75025 121393 196418 317811
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The Fibonacci numbers are the numbers in the following integer sequence.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

`    Fn = Fn-1 + Fn-2`

with seed values F1 = 1 and F2 = 1.

Below is the implementation of the above pattern :

## C++

 `// C++ Implementation for  ` `// Fibonacci triangle ` `#include ` `using` `namespace` `std; ` ` `  `// function to fill Fibonacci Numbers ` `// in f[] ` `void` `fib(``int` `f[], ``int` `N) ` `{ ` `    ``// 1st and 2nd number of the ` `    ``// series are 1 and 1 ` `    ``f = 1; ` `    ``f = 1; ` `     `  `    ``for` `(``int` `i = 3; i <= N; i++) ` `     `  `        ``// Add the previous 2 numbers ` `        ``// in the series and store it ` `        ``f[i] = f[i - 1] + f[i - 2]; ` `} ` ` `  `void` `fiboTriangle(``int` `n) ` `{ ` `    ``// Fill Fibonacci numbers in f[] using ` `    ``// fib(). We need N = n*(n+1)/2 Fibonacci ` `    ``// numbers to make a triangle of height ` `    ``// n ` `    ``int` `N = n*(n+1)/2; ` `    ``int` `f[N + 1]; ` `    ``fib(f, N); ` `     `  `    ``// To store next Fibonacci Number to print ` `    ``int` `fiboNum = 1; ` ` `  `    ``// for loop to keep track of ` `    ``// number of lines ` `    ``for` `(``int` `i = 1; i <= n;i++) ` `    ``{ ` `        ``// For loop to keep track of ` `        ``// numbers in each line ` `        ``for` `(``int` `j = 1;j <= i;j++) ` `            ``cout << f[fiboNum++] << ``" "``; ` `             `  `        ``cout << endl; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` `    ``fiboTriangle(n); ` `    ``return` `0; ` `} `

## Java

 `// Java Implementation for  ` `// Fibonacci triangle ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// function to fill Fibonacci Numbers ` `    ``// in f[] ` `    ``static` `void` `fib(``int` `f[], ``int` `N) ` `    ``{ ` `        ``// 1st and 2nd number of the ` `        ``// series are 1 and 1 ` `        ``f[``1``] = ``1``; ` `        ``f[``2``] = ``1``; ` `         `  `        ``for` `(``int` `i = ``3``; i <= N; i++) ` `         `  `            ``// Add the previous 2 numbers ` `            ``// in the series and store it ` `            ``f[i] = f[i - ``1``] + f[i - ``2``]; ` `    ``} ` `     `  `    ``static` `void` `fiboTriangle(``int` `n) ` `    ``{ ` `        ``// Fill Fibonacci numbers in f[] using ` `        ``// fib(). We need N = n*(n+1)/2 Fibonacci ` `        ``// numbers to make a triangle of height ` `        ``// n ` `        ``int` `N = n * (n + ``1``) / ``2``; ` `        ``int` `f[]=``new` `int``[N + ``1``]; ` `        ``fib(f, N); ` `         `  `        ``// To store next Fibonacci  ` `        ``// Number to print ` `        ``int` `fiboNum = ``1``; ` `     `  `        ``// for loop to keep track of ` `        ``// number of lines ` `        ``for` `(``int` `i = ``1``; i <= n; i++) ` `        ``{ ` `            ``// For loop to keep track of ` `            ``// numbers in each line ` `            ``for` `(``int` `j = ``1``; j <= i; j++) ` `                ``System.out.print(f[fiboNum++] + ``" "``); ` `                 `  `            ``System.out.println(); ` `        ``} ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``5``; ` `        ``fiboTriangle(n); ` `    ``} ` `} ` ` `  `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 Implementation for  ` `# Fibonacci triangle ` ` `  `     `  `# function to fill Fibonacci  ` `# Numbers in f[] ` `def` `fib(f, N) : ` `     `  `    ``# 1st and 2nd number of ` `    ``# the series are 1 and 1 ` `    ``f[``1``] ``=` `1` `    ``f[``2``] ``=` `1` `     `  `    ``for` `i ``in` `range``(``3``, N ``+` `1``) : ` `     `  `        ``# Add the previous 2 numbers ` `        ``# in the series and store it ` `        ``f[i] ``=` `f[i ``-` `1``] ``+` `f[i ``-` `2``] ` `         `  ` `  `def` `fiboTriangle(n) : ` `     `  `    ``# Fill Fibonacci numbers in ` `    ``# f[] using fib(). We need  ` `    ``# N = n*(n + 1)/2 Fibonacci ` `    ``# numbers to make a triangle  ` `    ``# of height n ` `    ``N ``=` `n ``*` `(n ``+` `1``) ``/``/` `2` `    ``f ``=``[``0``] ``*` `(N ``+` `1``) ` `    ``fib(f, N) ` `     `  `    ``# To store next Fibonacci  ` `    ``# Number to print ` `    ``fiboNum ``=` `1` ` `  `    ``# for loop to keep track of ` `    ``# number of lines ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) : ` `     `  `        ``# For loop to keep track of ` `        ``# numbers in each line ` `        ``for` `j ``in` `range``( ``1``, i ``+` `1``) : ` `         `  `            ``fiboNum ``=` `fiboNum ``+` `1` `            ``print``(f[fiboNum], ``" "``, end ``=` `"") ` `             `  `        ``print``() ` `         `  `# Driver code ` `n ``=` `5` `fiboTriangle(n) ` ` `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# Implementation for  ` `// Fibonacci triangle ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// function to fill Fibonacci Numbers ` `    ``// in f[] ` `    ``static` `void` `fib(``int` `[]f, ``int` `N) ` `    ``{ ` `        ``// 1st and 2nd number of the ` `        ``// series are 1 and 1 ` `        ``f = 1; ` `        ``f = 1; ` `         `  `        ``for` `(``int` `i = 3; i <= N; i++) ` `         `  `            ``// Add the previous 2 numbers ` `            ``// in the series and store it ` `            ``f[i] = f[i - 1] + f[i - 2]; ` `    ``} ` `     `  `    ``static` `void` `fiboTriangle(``int` `n) ` `    ``{ ` `        ``// Fill Fibonacci numbers in f[] using ` `        ``// fib(). We need N = n*(n+1)/2 Fibonacci ` `        ``// numbers to make a triangle of height ` `        ``// n ` `        ``int` `N = n * (n + 1) / 2; ` `        ``int` `[]f = ``new` `int``[N + 1]; ` `        ``fib(f, N); ` `         `  `        ``// To store next Fibonacci  ` `        ``// Number to print ` `        ``int` `fiboNum = 1; ` `     `  `        ``// for loop to keep track of ` `        ``// number of lines ` `        ``for` `(``int` `i = 1; i <= n; i++) ` `        ``{ ` `            ``// For loop to keep track of ` `            ``// numbers in each line ` `            ``for` `(``int` `j = 1; j <= i; j++) ` `                ``Console.Write(f[fiboNum++] + ``" "``); ` `                 `  `            ``Console.WriteLine(); ` `        ``} ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 5; ` `        ``fiboTriangle(n); ` `    ``} ` `} ` ` `  `/*This code is contributed by vt_m.*/`

## PHP

 ` `

Output:

```1
1 2
3 5 8
13 21 34 55
89 144 233 377 610
```

## tags:

Mathematical Fibonacci Mathematical Fibonacci