# 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 = 2
Output : 6
Triplets are : (0, 0, 2), (1, 0, 1), (0, 1, 1), (2, 0, 0), (0, 2, 0), (1, 1, 0)

Input : N = 50
Output : 1326

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

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 ` `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.. `

Output:

```1326
```

Time Complexity : O(1)

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