We are given a number n, we need to find n-th centered Icosahedral number.
Description: A centered icosahedral number is a centered figurate number that represents an icosahedron.
The first few centered icosahedral number series are :
1, 13, 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, 5083, 6525, 8217……………….
Mathematical Formula for nth Centered icosahedral number:
Examples :
Input : n = 4 Output : 309 Input : n = 12 Output : 6525
Below is the implementation of the above formula
C++
// C++ Program to find nth // Centered icosahedral number #include <bits/stdc++.h> using namespace std;
// Function to find // Centered icosahedral number int centeredIcosahedralNum( int n)
{ // Formula to calculate nth
// Centered icosahedral number
// and return it into main function.
return (2 * n + 1) * (5 * n * n + 5 * n + 3) / 3;
} // Driver Code int main()
{ int n = 10;
cout << centeredIcosahedralNum(n) << endl;
n = 12;
cout << centeredIcosahedralNum(n) << endl;
return 0;
} |
C
// C Program to find nth // Centered icosahedral number #include <stdio.h> // Function to find // Centered icosahedral number int centeredIcosahedralNum( int n)
{ // Formula to calculate nth
// Centered icosahedral number
// and return it into main function.
return (2 * n + 1) * (5 * n * n + 5 * n + 3) / 3;
} // Driver Code int main()
{ int n = 10;
printf ( "%d\n" ,centeredIcosahedralNum(n));
n = 12;
printf ( "%d\n" ,centeredIcosahedralNum(n));
return 0;
} // This code is contributed by kothavvsaakash. |
Java
// Java Program to find nth // Centered icosahedral number // Java Program to find nth Centered // icosahedral number import java.io.*;
class GFG {
// Function to find Centered
// icosahedral number
static int centeredIcosahedralNum( int n)
{
// Formula to calculate nth Centered
// icosahedral number and return it
// into main function.
return ( 2 * n + 1 ) * ( 5 * n * n +
5 * n + 3 ) / 3 ;
}
// Driver Code
public static void main (String[] args)
{
int n = 10 ;
System.out.println(
centeredIcosahedralNum(n));
n = 12 ;
System.out.println(
centeredIcosahedralNum(n));
}
} // This code is contributed by anuj_67. |
Python3
# Python program to find nth # Centered icosahedral number # Function to calculate # Centered icosahedral number def centeredIcosahedralNum(n):
# Formula to calculate nth
# Centered icosahedral number
return (( 2 * n + 1 ) *
( 5 * n * n + 5 * n + 3 ) / / 3 )
# Driver Code n = 10
print (centeredIcosahedralNum(n))
n = 12
print (centeredIcosahedralNum(n))
# This code is contributed by ajit. |
C#
// C# Program to find nth // Centered icosahedral number using System;
class GFG {
// Function to find Centered
// icosahedral number
static int centeredIcosahedralNum( int n)
{
// Formula to calculate nth Centered
// icosahedral number and return it
// into main function.
return (2 * n + 1) * (5 * n * n +
5 * n + 3) / 3;
}
// Driver Code
public static void Main ()
{
int n = 10;
Console.WriteLine(
centeredIcosahedralNum(n));
n = 12;
Console.WriteLine(
centeredIcosahedralNum(n));
}
} // This code is contributed by anuj_67. |
PHP
<?php // PHP Program to find nth // Centered icosahedral number // Function to find // Centered icosahedral number function centeredIcosahedralNum( $n )
{ // Formula to calculate nth
// Centered icosahedral number
// and return it into main function.
return (2 * $n + 1) * (5 *
$n * $n + 5 * $n + 3) / 3;
} // Driver Code $n = 10;
echo centeredIcosahedralNum( $n ), "\n" ;
$n = 12;
echo centeredIcosahedralNum( $n ), "\n" ;
// This code is contributed by m_kit ?> |
Javascript
<script> // Javascript Program to find nth // Centered icosahedral number // Function to find // Centered icosahedral number function centeredIcosahedralNum(n)
{ // Formula to calculate nth
// Centered icosahedral number
// and return it into main function.
return parseInt((2 * n + 1) * (5 * n * n + 5 * n + 3) / 3);
} // Driver Code let n = 10; document.write(centeredIcosahedralNum(n) + "<br>" );
n = 12; document.write(centeredIcosahedralNum(n)); // This code is contributed by souravmahato348. </script> |
Output :
3871 6525
Time Complexity: O(1)
Auxiliary Space: O(1)
Reference:
https://en.wikipedia.org/wiki/Centered_icosahedral_number