Centered tetrahedral number
Last Updated :
29 Mar, 2023
We are given integer n, we need to find n-th centered tetrahedral number.
Description: The centered tetrahedral number is a centered figurate number that represents a tetrahedron.
Tetrahedral Numbers: A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers.
The first few centered tetrahedral number series are:
1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….
Mathematical nth Term of centered tetrahedral number:
Examples :
Input : n = 3
Output : 35
Input : n = 9
Output : 589
Below is the implementation of above formula.
C++
#include <bits/stdc++.h>
using namespace std;
int centeredTetrahedralNumber( int n)
{
return (2 * n + 1) * (n * n + n + 3) / 3;
}
int main()
{
int n = 6;
cout << centeredTetrahedralNumber(n);
return 0;
}
|
C
#include <stdio.h>
int centeredTetrahedralNumber( int n)
{
return (2 * n + 1) * (n * n + n + 3) / 3;
}
int main()
{
int n = 6;
printf ( "%d" ,centeredTetrahedralNumber(n));
return 0;
}
|
Java
import java.io.*;
class GFG {
static int centeredTetrahedralNumber( int n)
{
return ( 2 * n + 1 ) * (n * n + n + 3 ) / 3 ;
}
public static void main (String[] args)
{
int n = 6 ;
System.out.println(
centeredTetrahedralNumber(n));
}
}
|
Python3
def centeredTetrahedralNumber(n):
return ( 2 * n + 1 ) * (n * n + n + 3 ) / / 3
n = 6
print (centeredTetrahedralNumber(n))
|
C#
using System;
class GFG {
static int centeredTetrahedralNumber( int n)
{
return (2 * n + 1) * (n * n + n + 3) / 3;
}
public static void Main ()
{
int n = 6;
Console.WriteLine(
centeredTetrahedralNumber(n));
}
}
|
PHP
<?php
function centeredTetrahedralNumber( $n )
{
return (2 * $n + 1) *
( $n * $n + $n + 3) / 3;
}
$n = 6;
echo centeredTetrahedralNumber( $n );
?>
|
Javascript
<script>
function centeredTetrahedralNumber(n)
{
return (2 * n + 1) * (n * n + n + 3) / 3;
}
var n = 6;
document.write(centeredTetrahedralNumber(n));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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