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 : 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;
}

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:

Time Complexity : O(1)

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