# 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

**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; ` `} ` |

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## 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 ` |

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## 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.. ` |

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**Output:**

1326

**Time Complexity :** O(1)

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