# Count non-negative triplets with sum equal to N

Given an integer **N**. The task is to find the number of different ordered triplets(a, b, c) of non-negative integers such that **a + b + c = N **.**Examples:**

Input :N = 2Output :6

Triplets are : (0, 0, 2), (1, 0, 1), (0, 1, 1), (2, 0, 0), (0, 2, 0), (1, 1, 0)Input :N = 50Output :1326

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**Approach :**

First, it is easy to see that for each non-negative integer **N**, the equation **a + b = N** can be satisfied by **(N+1)** different ordered pairs of **(a, b).** Now we can assign **c** values from **0** to **N** then the ordered pairs for **a+b** can be found. It will form a series of **N+1** natural numbers and its sum will give the count of triplets.

Below is the implementation of the above approach :

## C++

`// CPP program to find triplets count` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find triplets count` `int` `triplets(` `int` `N)` `{` ` ` `// Sum of first n+1 natural numbers` ` ` `return` `((N + 1) * (N + 2)) / 2;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `N = 50;` ` ` ` ` `// Function call` ` ` `cout << triplets(N);` ` ` ` ` `return` `0;` `}` |

## Java

`// Java program to find triplets count` `class` `GFG` `{` ` ` `// Function to find triplets count` `static` `int` `triplets(` `int` `N)` `{` ` ` `// Sum of first n+1 natural numbers` ` ` `return` `((N + ` `1` `) * (N + ` `2` `)) / ` `2` `;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `50` `;` ` ` `System.out.println(triplets(N));` `}` `}` `// This code is contributed` `// by PrinciRaj1992` |

## Python3

`# Python3 program to find triplets count` `# Function to find triplets count` `def` `triplets(N):` ` ` `# Sum of first n+1 natural numbers` ` ` `return` `((N ` `+` `1` `) ` `*` `(N ` `+` `2` `)) ` `/` `/` `2` `;` `# Driver code` `N ` `=` `50` `;` ` ` `# Function call` `print` `(triplets(N))` `# This code is contributed by nidhi` |

## C#

`// C# program to find triplets count` `using` `System;` `class` `GFG` `{` ` ` `// Function to find triplets count` `static` `int` `triplets(` `int` `N)` `{` ` ` `// Sum of first n+1 natural numbers` ` ` `return` `((N + 1) * (N + 2)) / 2;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `N = 50;` ` ` `Console.WriteLine(triplets(N));` `}` `}` `// This code is contributed` `// by anuj_67..` |

## Javascript

`<script>` ` ` `// Javascript program to find triplets count ` ` ` ` ` `// Function to find triplets count` ` ` `function` `triplets(N)` ` ` `{` ` ` `// Sum of first n+1 natural numbers` ` ` `return` `((N + 1) * (N + 2)) / 2;` ` ` `}` ` ` ` ` `let N = 50;` ` ` `document.write(triplets(N));` ` ` `</script>` |

**Output:**

1326

**Time Complexity :** O(1)