Find the sum of the first Nth Centered Tridecagonal Numbers
Given a number N, the task is to find the sum of first N Centered tridecagonal number.
A Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot in the successive tridecagonal(13 sided polygon) layer. The first few Centered tridecagonal numbers are 1, 14, 40, 79 …
Examples:
Input: N = 3
Output: 55
Explanation:
1, 14 and 40 are the first three Centered tridecagonal number.
1 + 14 + 40 = 55.Input: N = 5
Output: 265
Approach:
- Initially, we need to create a function which will help us to calculate the Nth Centered tridecagonal number.
- Now, Run a loop starting from 1 to N, and find the Centered tridecagonal numbers in this range.
- Add all the above calculated Centered tridecagonal numbers.
- Finally, display the sum of the first N Centered tridecagonal numbers.
Below is the implementation of the above approach:
C++
// C++ program to find the sum of // the first Nth centered // tridecagonal number #include<bits/stdc++.h> using namespace std; // Function to calculate the // N-th centered tridecagonal // number int Centered_tridecagonal_num( int n) { // Formula to calculate // Nth centered tridecagonal // number & return it return (13 * n * (n - 1) + 2) / 2; } // Function to find the sum // of the first N centered // tridecagonal numbers int sum_Centered_tridecagonal_num( int n) { // Variable to store // the sum int summ = 0; // Loop to iterate and find the // sum of first N centered // tridecagonal numbers for ( int i = 1; i <= n; i++) { summ += Centered_tridecagonal_num(i); } return summ ; } // Driver code int main() { int n = 5; cout << sum_Centered_tridecagonal_num(n) << endl; return 0; } // This code is contributed by rutvik_56 |
Java
// Java program to find the sum of // the first Nth centered // tridecagonal number class GFG{ // Function to calculate the // N-th centered tridecagonal // number public static int Centered_tridecagonal_num( int n) { // Formula to calculate // Nth centered tridecagonal // number & return it return ( 13 * n * (n - 1 ) + 2 ) / 2 ; } // Function to find the sum // of the first N centered // tridecagonal numbers public static int sum_Centered_tridecagonal_num( int n) { // Variable to store // the sum int summ = 0 ; // Loop to iterate and find the // sum of first N centered // tridecagonal numbers for ( int i = 1 ; i <= n; i++) { summ += Centered_tridecagonal_num(i); } return summ ; } // Driver code public static void main(String[] args) { int n = 5 ; System.out.println(sum_Centered_tridecagonal_num(n)); } } // This code is contributed by divyeshrabadiya07 |
Python3
# Program to find the sum of # the first Nth # Centered_tridecagonal number # Function to calculate the # N-th Centered tridecagonal # number def Centered_tridecagonal_num(n): # Formula to calculate # Nth Centered tridecagonal # number & return it return ( 13 * n * (n - 1 ) + 2 ) / / 2 # Function to find the sum # of the first N # Centered tridecagonal # numbers def sum_Centered_tridecagonal_num(n) : # Variable to store # the sum summ = 0 # Loop to iterate and find the # sum of first N Centered # tridecagonal numbers for i in range ( 1 , n + 1 ): summ + = Centered_tridecagonal_num(i) return summ # Driver Code if __name__ = = '__main__' : n = 5 print (sum_Centered_tridecagonal_num(n)) |
C#
// C# program to find the sum of // the first Nth centered // tridecagonal number using System; class GFG{ // Function to calculate the // N-th centered tridecagonal // number public static int Centered_tridecagonal_num( int n) { // Formula to calculate // Nth centered tridecagonal // number & return it return (13 * n * (n - 1) + 2) / 2; } // Function to find the sum // of the first N centered // tridecagonal numbers public static int sum_Centered_tridecagonal_num( int n) { // Variable to store // the sum int summ = 0; // Loop to iterate and find the // sum of first N centered // tridecagonal numbers for ( int i = 1; i <= n; i++) { summ += Centered_tridecagonal_num(i); } return summ; } // Driver code public static void Main() { int n = 5; Console.WriteLine(sum_Centered_tridecagonal_num(n)); } } // This code is contributed by Code_Mech |
Javascript
<script> // Javascript program to find the sum of // the first Nth centered // tridecagonal number // Function to calculate the // N-th centered tridecagonal // number function Centered_tridecagonal_num(n) { // Formula to calculate // Nth centered tridecagonal // number & return it return (13 * n * (n - 1) + 2) / 2; } // Function to find the sum // of the first N centered // tridecagonal numbers function sum_Centered_tridecagonal_num(n) { // Variable to store // the sum let summ = 0; // Loop to iterate and find the // sum of first N centered // tridecagonal numbers for (let i = 1; i <= n; i++) { summ += Centered_tridecagonal_num(i); } return summ ; } let n = 5; document.write(sum_Centered_tridecagonal_num(n)); // This code is contributed by divyesh072019. </script> |
Output:
265
Time complexity: O(N).
Auxiliary Space: O(1) as it is using constant space for variables