# Count the total number of triangles after Nth operation

• Difficulty Level : Basic
• Last Updated : 19 Apr, 2021

Given an equilateral triangle, the task is to compute the total number of triangles after performing the following operation N times.
For every operation, the uncolored triangles are taken and divided into 4 equal equilateral triangles. Every inverted triangle formed is colored. Refer to the below figure for more details.
For N=1 the triangle formed is: Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

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For N=2 the triangle formed is: Examples:

Input :N = 10
Output : 118097
Input : N = 2
Output : 17

Approach:

• At every operation, 3 uncolored triangles, 1 colored triangle and the triangle itself is formed
• On writing the above statement mathematically; count of triangles at Nth move = 3 * count of triangles at (N-1)th move + 2
• Therefore, initializing a variable curr = 1 and tri_count = 0
• Next, a loop is iterated from 1 to N
• For every iteration, the operation mentioned above is performed.
• Finally, the tri_count is returned

Below is the implementation of the above approach:

## C++

 `#include ``using` `namespace` `std;``// function to return the``// total no.of Triangles``int` `CountTriangles(``int` `n)``{``    ``int` `curr = 1;``    ``int` `Tri_count = 0;``    ``for` `(``int` `i = 1; i <= n; i++) {``        ``// For every subtriangle formed``        ``// there are possibilities of``        ``// generating (curr*3)+2` `        ``Tri_count = (curr * 3) + 2;``        ``// Changing the curr value to Tri_count``        ``curr = Tri_count;``    ``}``    ``return` `Tri_count;``}` `// driver code``int` `main()``{``    ``int` `n = 10;``    ``cout << CountTriangles(n);``    ``return` `0;``}`

## Java

 `class` `Gfg {``    ``// Method to return the``    ``// total no.of Triangles``    ``public` `static` `int` `CountTriangles(``int` `n)``    ``{``        ``int` `curr = ``1``;``        ``int` `Tri_count = ``0``;``        ``for` `(``int` `i = ``1``; i <= n; i++) {``            ``// For every subtriangle formed``            ``// there are possibilities of``            ``// generating (curr*3)+2` `            ``Tri_count = (curr * ``3``) + ``2``;``            ``// Changing the curr value to Tri_count``            ``curr = Tri_count;``        ``}``        ``return` `Tri_count;``    ``}` `    ``// driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``10``;``        ``System.out.println(CountTriangles(n));``    ``}``}`

## Python

 `# Function to return the``# total no.of Triangles``def` `countTriangles(n):``    ` `    ``curr ``=` `1``    ``Tri_count ``=` `0``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``            ` `        ``# For every subtriangle formed``        ``# there are possibilities of``        ``# generating (curr * 3)+2``        ``Tri_count ``=` `(curr ``*` `3``) ``+` `2``        ``# Changing the curr value to Tri_count``        ``curr ``=` `Tri_count``    ``return` `Tri_count``    ` `n ``=` `10``print``(countTriangles(n))`

## C#

 `using` `System;` `class` `Gfg``{``    ``// Method to return the``    ``// total no.of Triangles``    ``public` `static` `int` `CountTriangles(``int` `n)``    ``{``        ``int` `curr = 1;``        ``int` `Tri_count = 0;``        ``for` `(``int` `i = 1; i <= n; i++)``        ``{``            ``// For every subtriangle formed``            ``// there are possibilities of``            ``// generating (curr*3)+2``            ``Tri_count = (curr * 3) + 2;``            ` `            ``// Changing the curr value to Tri_count``            ``curr = Tri_count;``        ``}``        ``return` `Tri_count;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int` `n = 10;``        ``Console.WriteLine(CountTriangles(n));``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`118097`

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