# Sum of the first N Pronic Numbers

Given a number N, the task is to find the sum of the first N Pronic Numbers.

The numbers that can be arranged to form a rectangle are called Rectangular Numbers (also known as Pronic numbers). The first few rectangular numbers are:
0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 . . . .

Examples:

Input: N = 4
Output: 20
Explanation:
0, 2, 6, 12 are the first 4 pronic numbers.

Input: N = 3
Output: 8

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

Approach:

Let, the Nth term be denoted by TN. This problem can easily be solved by splitting each term as follows:     Therefore:

SN = Sum of N Pronic Numbers Below is the implementation of the above approach:

## C++

 // C++ implementation to find   // sum of first N terms  #include  using namespace std;     // Function to calculate the sum  int calculateSum(int N)  {         return N * (N - 1) / 2             + N * (N - 1)                   * (2 * N - 1) / 6;  }     // Driver code  int main()  {      int N = 3;         cout << calculateSum(N);         return 0;  }

## Java

 // Java implementation implementation to find   // sum of first N terms   class GFG{          // Function to calculate the sum   static int calculateSum(int N)   {              return N * (N - 1) / 2 + N * (N - 1) *             (2 * N - 1) / 6;   }          // Driver code   public static void main (String[] args)   {       int N = 3;              System.out.println(calculateSum(N));   }   }      // This code is contributed by Pratima Pandey

## Python3

 # Python3 implementation to find   # sum of first N terms     # Function to calculate the sum  def calculateSum(N):         return (N * (N - 1) // 2 +              N * (N - 1) * (2 *                   N - 1) // 6);     # Driver code  N = 3;  print(calculateSum(N));     # This code is contributed by Code_Mech

## C#

 // C# implementation implementation to find   // sum of first N terms   using System;  class GFG{          // Function to calculate the sum   static int calculateSum(int N)   {              return N * (N - 1) / 2 + N * (N - 1) *                          (2 * N - 1) / 6;   }          // Driver code   public static void Main()   {       int N = 3;              Console.Write(calculateSum(N));   }   }      // This code is contributed by Code_Mech

Output:

8


Time complexity: O(1).

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : dewantipandeydp, Code_Mech

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.