Centered triangular number
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 centre and all other dots surrounding the centre 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 centre 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++
// CPP Program to find the // nth Centered Trigunal number #include using namespace std; // function for Centered // Trigunal number int Centered_Trigunal_num(int n) { // formula for find Centered // Trigunal number nth term return (3 * n * n + 3 * n + 2) / 2; } // Driver Code int main() { // For 3rd Centered Trigunal number int n = 3; cout << Centered_Trigunal_num(n) << endl; // For 12th Centered Trigunal number n = 12; cout << Centered_Trigunal_num(n) << endl; return 0; } |
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Java
// Java Program to find // the nth Centered // Triangular number import java.io.*; class GFG { // function for Centered // Trigunal number static int Centered_Trigunal_num(int n) { // formula for find Centered // Trigunal number nth term return (3 * n * n + 3 * n + 2) / 2; } // Driver Code public static void main (String[] args) { // For 3rd Centered // Trigunal number int n = 3; System.out.println(Centered_Trigunal_num(n)); // For 12th Centered // Trigunal number n = 12; System.out.println(Centered_Trigunal_num(n)); } } // This code is contributed by ajit |
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Python3
# Program to find nth # Centered Trigunal number def Centered_Trigunal_num(n) : # Formula to calculate nth # Centered Trigunal number return (3 * n * n + 3 * n + 2) // 2 # Driver Code if __name__ == '__main__' : # For 3rd Centered # Trigunal number n = 3 print(Centered_Trigunal_num(n)) # For 12th Centered # Trigunal number n = 12 print(Centered_Trigunal_num(n)) # This code is contributed # by akt_mit |
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C#
// C# Program to find // the nth Centered // Triangular number using System; class GFG { // function for Centered // Trigunal number static int Centered_Trigunal_num(int n) { // formula for find Centered // Trigunal number nth term return (3 * n * n + 3 * n + 2) / 2; } // Driver Code static public void Main () { // For 3rd Centered // Trigunal number int n = 3; Console.WriteLine(Centered_Trigunal_num(n)); // For 12th Centered // Trigunal number n = 12; Console.WriteLine(Centered_Trigunal_num(n)); } } // This code is contributed by akt_mit |
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PHP
<?php // PHP Program to find the //nth Centered Trigunal number // function for Centered // Trigunal number function Centered_Trigunal_num($n) { // formula for find Centered // Trigunal number nth term return (3 * $n * $n + 3 * $n + 2) / 2; } // Driver Code // For 3rd Centered Trigunal number $n = 3; echo Centered_Trigunal_num($n), "\n" ; // For 12th Centered Trigunal number $n = 12; echo Centered_Trigunal_num($n), "\n"; // This code is contributed by aj_36 ?> |
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Output :
19 235
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