# Count non-negative triplets with sum equal to N

• Last Updated : 15 Mar, 2021

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 :
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

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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 ``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

 ``
Output:
`1326`

Time Complexity : O(1)

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