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# Sum of first N Star Numbers

Given a number N, the task is to find the sum of the first N star numbers
The first few star numbers are 1, 13, 37, 73,..
Examples:

Input: N = 2
Output: 14
Explanation: 1, 13 are the first two star numbers.

Input: N = 3
Output: 51

Approach 1:

1. Nth Star number is given as
2. Run a loop from 1 to N, to find the first N star numbers.
3. Add all the above-calculated star numbers.
4. Return the sum.

Below is the implementation of the above approach:

## C++

 // C++ program to find the sum of  // the first N Star Number #include  using namespace std;    // Function to find the N-th  // Star Number  int star_num(int n)  {            // Formula to calculate nth      // Star Number     return (6 * n * n - 6 * n + 1); }    // Function to find the sum of the  // first N Star Number int sum_star_num(int n)  {            // Variable to store the sum      int summ = 0;            // Iterating from 1 to N      for(int i = 1; i < n + 1; i++)      {                    // Finding the sum          summ += star_num(i);     }      return summ;  }    // Driver code  int main()  {      int n = 3;            cout << sum_star_num(n);  }    // This code is contributed by spp____

## Java

 // Java program to find the sum of  // the first N Star Number class GFG{   // Function to find the N-th  // Star Number  static int star_num(int n)  {            // Formula to calculate nth      // Star Number     return (6 * n * n - 6 * n + 1); }    // Function to find the sum of the  // first N Star Number static int sum_star_num(int n)  {            // Variable to store the sum      int summ = 0;            // Iterating from 1 to N      for(int i = 1; i < n + 1; i++)      {                    // Finding the sum          summ += star_num(i);     }      return summ;  }    // Driver code  public static void main(String[] args) {      int n = 3;            System.out.println(sum_star_num(n)); } }    // This code is contributed by rock_cool

## Python3

 # Python3 program to find the  # sum of the first N   # star numbers   # Function to find the  # N-th star  # number  def star_num(n):        # Formula to calculate       # nth star      # number     return (6 * n * n - 6 * n + 1)      # Function to find the sum of  # the first N star numbers  def sum_star_num(n) :            # Variable to store     # the sum     summ = 0           # Iterating in the range      # 1 to N     for i in range(1, n + 1):         summ += star_num(i)           return summ     # Driver code  n = 3 print(sum_star_num(n))

## C#

 // C# program to find the sum of  // the first N Star Number using System; class GFG{   // Function to find the N-th  // Star Number  static int star_num(int n)  {            // Formula to calculate nth      // Star Number     return (6 * n * n - 6 * n + 1); }    // Function to find the sum of the  // first N Star Number static int sum_star_num(int n)  {            // Variable to store the sum      int summ = 0;            // Iterating from 1 to N      for(int i = 1; i < n + 1; i++)      {                    // Finding the sum          summ += star_num(i);     }      return summ;  }    // Driver code  public static void Main(String[] args) {      int n = 3;            Console.WriteLine(sum_star_num(n)); } }    // This code is contributed by gauravrajput1

## Javascript

 

Output

51

Time complexity: O(N).
Auxiliary Space: O(1)

Efficient Approach:

• Nth star number is given as
• So, the sum of the first N Star Numbers is
Sum =
Sum =
Sum =
• Calculate the sum and return.

Below is the implementation of the above approach:

## C++

 // C++ program to find the  // sum of the first N  // star numbers #include    using namespace std;   // Function to find the // sum of the first N // star number int sum_star_num(int n)  {           // Variable to store     // the sum     int summ = 2 * n * (n + 1) * (n - 1) + n;           return summ; }   // Driver code int main() {     int n = 3;           cout << sum_star_num(n);     return 0; }   // This code is contributed by Amit Katiyar

## Java

 // Java program to find the  // sum of the first N   // star numbers class GFG{           // Function to find the     // sum of the first N     // star number     static int sum_star_num(int n)      {           // Variable to store         // the sum         int summ = 2 * n * (n + 1) * (n - 1) + n;           return summ;     }       // Driver code     public static void main(String[] args)      {         int n = 3;         System.out.println(sum_star_num(n));     } }   // This code is contributed by PrinciRaj1992

## Python3

 # Python3 program to find the  # sum of the first N   # star numbers   # Function to find the  # sum of the first N # star number  def sum_star_num(n) :            # Variable to store     # the sum     summ = 2 * n*(n + 1)*(n-1) + n           return summ     # Driver code  n = 3 print(sum_star_num(n))

## C#

 // C# program to find the  // sum of the first N  // star numbers using System;   class GFG{       // Function to find the // sum of the first N // star number static int sum_star_num(int n)  {       // Variable to store     // the sum     int summ = 2 * n * (n + 1) * (n - 1) + n;       return summ; }   // Driver code public static void Main(String[] args)  {     int n = 3;           Console.WriteLine(sum_star_num(n)); } }   // This code is contributed by PrinciRaj1992

## Javascript

 

Output

51

Time complexity: O(1).
Auxiliary Space: O(1)

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