# 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

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

Approach 1:

1. Nth Star number is given as 2. Run a loop from 1 to N, to find 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

Output:

51


Time complexity: O(N).

Efficient Approach:

• We already know , , and • Nth star number is given as • So, the sum of 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

Output:

51


Time complexity: O(1).

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