# Count the total number of triangles after Nth operation

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:

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For **N=2** the triangle formed is:

**Examples:**

Input :N = 10Output :118097Input :N = 2Output :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 = 1andtri_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 <bits/stdc++.h>` `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

`<script>` ` ` `// Method to return the` ` ` `// total no.of Triangles` ` ` `function` `CountTriangles(n)` ` ` `{` ` ` `var` `curr = 1;` ` ` `var` `Tri_count = 0;` ` ` `for` `(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` ` ` `var` `n = 10;` ` ` `document.write(CountTriangles(n));` `// This code is contributed by aashish1995` `</script>` |

**Output:**

118097