Find the sum of the first N Centered Dodecagonal Number
Given a number N, the task is to find the sum of first N Centered Dodecagonal Number.
The first few Centered Dodecagonal Numbers are 1, 13, 37, 73, 121, 181 …
Examples:
Input: N = 3
Output: 51
Explanation:
1, 13 and 37 are the first three centered Dodecagonal number.
Input: N = 5
Output: 245
Approach:
- Initially, create a function which will help us to calculate the Nth Centered Dodecagonal number.
- Run a loop starting from 1 to N, to find i-th Centered Dodecagonal number.
- Add all the above calculated Centered Dodecagonal numbers.
- Finally, display the sum of the first N Centered Dodecagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum // of the first N Centered // Dodecagonal number #include <bits/stdc++.h> using namespace std; // Function to find the N-th // Centered Dodecagonal number int Centered_Dodecagonal_num( int n) { // Formula to calculate nth // Centered_Dodecagonal number return 6 * n * (n - 1) + 1; } // Function to find the sum of the first // N Centered_Dodecagonal number int sum_Centered_Dodecagonal_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 += Centered_Dodecagonal_num(i); } return summ; } // Driver code int main() { int n = 5; cout << sum_Centered_Dodecagonal_num(n); } // This code is contributed by coder001 |
Java
// Java program to find the sum of the // first N centered dodecagonal number class GFG { // Function to find the N-th // centered dodecagonal number static int Centered_Dodecagonal_num( int n) { // Formula to calculate nth // Centered_Dodecagonal number return 6 * n * (n - 1 ) + 1 ; } // Function to find the sum of the first // N Centered_Dodecagonal number static int sum_Centered_Dodecagonal_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 += Centered_Dodecagonal_num(i); } return summ; } // Driver code public static void main (String[] args) { int n = 5 ; System.out.print(sum_Centered_Dodecagonal_num(n)); } } // This code is contributed by AnkitRai01 |
Python3
# Python3 program to find the sum # of the first N centered # Dodecagonal number # Function to find the # N-th Centered Dodecagonal # number def Centered_Dodecagonal_num(n): # Formula to calculate # nth Centered_Dodecagonal # number return 6 * n * (n - 1 ) + 1 # Function to find the # sum of the first N # Centered_Dodecagonal # number def sum_Centered_Dodecagonal_num(n) : # Variable to store the # sum summ = 0 # Iterating from 1 to N for i in range ( 1 , n + 1 ): # Finding the sum summ + = Centered_Dodecagonal_num(i) return summ # Driver code if __name__ = = '__main__' : n = 5 print (sum_Centered_Dodecagonal_num(n)) |
C#
// C# program to find the sum of the // first N centered dodecagonal number using System; class GFG{ // Function to find the N-th // centered dodecagonal number static int Centered_Dodecagonal_num( int n) { // Formula to calculate nth // Centered_Dodecagonal number return 6 * n * (n - 1) + 1; } // Function to find the sum of the first // N Centered_Dodecagonal number static int sum_Centered_Dodecagonal_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 += Centered_Dodecagonal_num(i); } return summ; } // Driver code public static void Main() { int n = 5; Console.Write(sum_Centered_Dodecagonal_num(n)); } } // This code is contributed by Code_Mech |
Javascript
<script> // Javascript program to find the sum // of the first N Centered // Dodecagonal number // Function to find the N-th // Centered Dodecagonal number function Centered_Dodecagonal_num(n) { // Formula to calculate nth // Centered_Dodecagonal number return 6 * n * (n - 1) + 1; } // Function to find the sum of the first // N Centered_Dodecagonal number function sum_Centered_Dodecagonal_num(n) { // Variable to store the sum let summ = 0; // Iterating from 1 to N for (let i = 1; i < n + 1; i++) { // Finding the sum summ += Centered_Dodecagonal_num(i); } return summ; } let n = 5; document.write(sum_Centered_Dodecagonal_num(n)); </script> |
Output:
245
Time Complexity: O(N).
Auxiliary Space: O(1) since constant variables are being used