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
Approach:
Let, the Nth term be denoted by TN. This problem can easily be solved by splitting each term as follows:
Therefore:
// C++ implementation to find // sum of first N terms #include <bits/stdc++.h> 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 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 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# 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 |
// JS implementation to find // sum of first N terms // Function to calculate the sum function calculateSum(N)
{ return Math.floor(N * (N - 1) / 2) + Math.floor(N * (N - 1) * (2 * N - 1) / 6);
} // Driver code let N = 3; console.log(calculateSum(N)); // This code is contributed by phasing17 |
Output
8
Time complexity: O(1).
Auxiliary Space: O(1)