Find the sum of the first N Centered Octagonal Number
Given a number N, the task is to find the sum of the first N Centered Octagonal Numbers.
The first few Centered Octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …
Examples:
Input: N = 3
Output: 35
Explanation:
1, 9 and 25 are the first three Centered Octagonal numbers.Input: N = 5
Output: 165
Approach:
- Initially, we need to create a function that will help us to calculate the Nth centered octagonal numbers.
- Now, run a loop starting from 1 to N, to find ith centered octagonal numbers.
- Add all the above calculated centered octagonal numbers.
- Finally, display the sum of the first N-centered octagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum of the // first N centered octagonal number #include<bits/stdc++.h> using namespace std; // Function to find the N-th centered // octagonal number int center_Octagonal_num( int n) { // Formula to calculate // nth centered octagonal // number return (4 * n * n - 4 * n + 1); } // Function to find the sum of the first // N centered octagonal numbers int sum_center_Octagonal_num( int n) { // Variable to store // the sum int summ = 0; // Iterating through the range // 1 to N for ( int i = 1; i < n + 1; i++) { summ += center_Octagonal_num(i); } return summ; } // Driver Code int main() { int n = 5; cout << (sum_center_Octagonal_num(n)); return 0; } // This code is contributed by PratikBasu |
Java
// Java program to find the sum of the // first N centered octagonal number class GFG { // Function to find N-th centered // octagonal number static int center_Octagonal_num( int n) { // Formula to calculate // nth centered octagonal // number return ( 4 * n * n - 4 * n + 1 ); } // Function to find the // sum of the first N // centered octagonal // numbers static int sum_center_Octagonal_num( int n) { // Variable to store // the sum int summ = 0 ; // Iterating through the first N // numbers for ( int i = 1 ; i < n + 1 ; i++) { summ += center_Octagonal_num(i); } return summ; } // Driver code public static void main(String[] args) { int n = 5 ; System.out.println(sum_center_Octagonal_num(n)); } } // This code is contributed by Princi Singh |
Python3
# Python3 program to find the # sum of the first N # Centered Octagonal number # Function to find N-th # Centered Octagonal # number def center_Octagonal_num(n): # Formula to calculate # nth centered Octagonal # number return ( 4 * n * n - 4 * n + 1 ) # Function to find the # sum of the first N # Centered Octagonal # numbers def sum_center_Octagonal_num(n) : # Variable to store # the sum summ = 0 # Iterating through the first N # numbers for i in range ( 1 , n + 1 ): summ + = center_Octagonal_num(i) return summ # Driver code if __name__ = = '__main__' : n = 5 print (sum_center_Octagonal_num(n)) |
C#
// C# program to find the sum of the // first N centered octagonal number using System; class GFG{ // Function to find N-th centered // octagonal number static int center_Octagonal_num( int n) { // Formula to calculate // nth centered octagonal // number return (4 * n * n - 4 * n + 1); } // Function to find the sum of // the first N centered octagonal // numbers static int sum_center_Octagonal_num( int n) { // Variable to store // the sum int summ = 0; // Iterating through the first N // numbers for ( int i = 1; i < n + 1; i++) { summ += center_Octagonal_num(i); } return summ; } // Driver code public static void Main() { int n = 5; Console.WriteLine(sum_center_Octagonal_num(n)); } } // This code is contributed by Akanksha_Rai |
Javascript
<script> // Javascript program to find the sum of the // first N centered octagonal number // Function to find the N-th centered // octagonal number function center_Octagonal_num(n) { // Formula to calculate // nth centered octagonal // number return (4 * n * n - 4 * n + 1); } // Function to find the sum of the first // N centered octagonal numbers function sum_center_Octagonal_num(n) { // Variable to store // the sum let summ = 0; // Iterating through the range // 1 to N for (let i = 1; i < n + 1; i++) { summ += center_Octagonal_num(i); } return summ; } let n = 5; document.write(sum_center_Octagonal_num(n)); </script> // This code is contributed by divyeshrabadiya07. |
Output
165
Time Complexity: O(N)
Auxiliary Space: O(1)