Centered triangular number
Last Updated :
29 Mar, 2023
Given an integer n, find the nth Centered triangular number.
Centered Triangular Number is a centered polygonal number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers [Source : Wiki ]
Pictorial Representation :
The first few centered triangular number series are :
1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460………………………..
Examples:
Input : n = 1
Output : 4
Explanation :
A dot in the center and 3 dots forming the
triangle outside it, thus 4.
Input : n = 6
Output : 64
Input : n = 10
Output : 166
Approach
nth Term of centered triangular number is given by:
Basic Implementation of the above approach:
C++
#include <iostream>
using namespace std;
int Centered_Triangular_num( int n)
{
return (3 * n * n + 3 * n + 2) / 2;
}
int main()
{
int n = 3;
cout << Centered_Triangular_num(n) << endl;
n = 12;
cout << Centered_Triangular_num(n) << endl;
return 0;
}
|
C
#include <stdio.h>
int Centered_Triangular_num( int n)
{
return (3 * n * n + 3 * n + 2) / 2;
}
int main()
{
int n = 3;
printf ( "%d\n" ,Centered_Triangular_num(n));
n = 12;
printf ( "%d\n" ,Centered_Triangular_num(n));
return 0;
}
|
Java
import java.io.*;
class GFG
{
static int Centered_Triangular_num( int n)
{
return ( 3 * n * n +
3 * n + 2 ) / 2 ;
}
public static void main (String[] args)
{
int n = 3 ;
System.out.println(Centered_Triangular_num(n));
n = 12 ;
System.out.println(Centered_Triangular_num(n));
}
}
|
Python3
def Centered_Triangular_num(n) :
return ( 3 * n * n +
3 * n + 2 ) / / 2
if __name__ = = '__main__' :
n = 3
print (Centered_Triangular_num(n))
n = 12
print (Centered_Triangular_num(n))
|
C#
using System;
class GFG
{
static int Centered_Triangular_num( int n)
{
return (3 * n * n +
3 * n + 2) / 2;
}
static public void Main ()
{
int n = 3;
Console.WriteLine(Centered_Triangular_num(n));
n = 12;
Console.WriteLine(Centered_Triangular_num(n));
}
}
|
PHP
<?php
function Centered_Triangular_num( $n )
{
return (3 * $n * $n + 3 * $n + 2) / 2;
}
$n = 3;
echo Centered_Triangular_num( $n ), "\n" ;
$n = 12;
echo Centered_Triangular_num( $n ), "\n" ;
?>
|
Javascript
<script>
function Centered_Triangular_num(n)
{
return (3 * n * n + 3 * n + 2) / 2;
}
var n = 3;
document.write(Centered_Triangular_num(n)+ "<br/>" );
n = 12;
document.write(Centered_Triangular_num(n)+ "<br/>" );
</script>
|
Output :
19
235
Time Complexity: O(1)
Auxiliary Space: O(1)
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