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Second hexagonal numbers

  • Last Updated : 13 Jul, 2021

The Second hexagonal numbers series can be represented as 
 

3, 10, 21, 36, 55, 78, 105, 136, 171, 210, 253, …..

 

Nth term

Given an integer N. The task is to find the N-th term of the given series.
Examples
 



Input: N = 1 
Output: 3
Input: N = 4 
Output: 36 
 

 

Approach: The idea is to find the general term for the Second hexagonal numbers. Below is the computation of the general term for second hexagonal numbers: 
 

1st Term = 1 * (2*1 + 1) = 3 
2nd term = 2 * (2*2 + 1) = 10 
3rd term = 3 * (2*3 + 1) = 21 
4th term = 4 * (2*4 + 1) = 36 



Nth term = n * (2*n + 1) 
Therefore, the Nth term of the series is given as 

n * (2*n + 1)
 

 

 

Below is the implementation of above approach: 
 

C++




// C++ implementation to
// find N-th term
// in the series
#include <iostream>
#include <math.h>
using namespace std;
 
// Function to find N-th term
// in the series
void findNthTerm(int n)
{
    cout << n * (2 * n + 1) << endl;
}
 
// Driver code
int main()
{
    int N = 4;
    findNthTerm(N);
 
    return 0;
}

Java




// Java implementation to
// find N-th term
// in the series
class GFG{
     
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    System.out.print(n * (2 * n + 1));
}
 
// Driver code
public static void main (String[] args)
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Ritik Bansal

Python3




# Python3 implementation to
# find N-th term
# in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
    print(n * (2 * n + 1))
 
# Driver code
N = 4
 
# Function call
findNthTerm(N)
 
# This code is contributed by Vishal Maurya

C#




// C# implementation to
// find N-th term
// in the series
using System;
class GFG{
     
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
    Console.Write(n * (2 * n + 1));
}
 
// Driver code
public static void Main()
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
 
// Javascript implementation to
// find N-th term
// in the series
 
// Function to find N-th term
// in the series
function findNthTerm(n)
{
    document.write(n * (2 * n + 1));
}
 
// Driver code
N = 4;
findNthTerm(N);
 
</script>
Output: 
36
 

Time Complexity: O(1)
Auxiliary Space: O(1)

Reference:OEIS
 

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