Centered triangular number

• Difficulty Level : Basic
• Last Updated : 03 Aug, 2021

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++

 // C++ Program to find the// nth Centered Triangular number#include using namespace std; // function for Centered// Triangular numberint Centered_Triangular_num(int n){    // formula for find Centered    // Triangular number nth term    return (3 * n * n + 3 * n + 2) / 2;} // Driver Codeint main(){    // For 3rd Centered Triangular number    int n = 3;    cout << Centered_Triangular_num(n) << endl;     // For 12th Centered Triangular number    n = 12;    cout << Centered_Triangular_num(n) << endl;     return 0;}

Java

 // Java Program to find// the nth Centered// Triangular numberimport java.io.*; class GFG{     // function for Centered// Triangular numberstatic int Centered_Triangular_num(int n){    // formula for find Centered    // Triangular number nth term    return (3 * n * n +            3 * n + 2) / 2;} // Driver Codepublic static void main (String[] args){ // For 3rd Centered// Triangular numberint n = 3;System.out.println(Centered_Triangular_num(n)); // For 12th Centered// Triangular numbern = 12;System.out.println(Centered_Triangular_num(n));}} // This code is contributed by ajit

Python3

 # Program to find nth# Centered Triangular number def Centered_Triangular_num(n) :         # Formula to calculate nth    # Centered Triangular number    return (3 * n * n +            3 * n + 2) // 2 # Driver Codeif __name__ == '__main__' :     # For 3rd Centered    # Triangular number        n = 3    print(Centered_Triangular_num(n))         # For 12th Centered    # Triangular number    n = 12    print(Centered_Triangular_num(n))                                  # This code is contributed# by akt_mit

C#

 // C# Program to find// the nth Centered// Triangular numberusing System; class GFG{ // function for Centered// Triangular numberstatic int Centered_Triangular_num(int n){    // formula for find Centered    // Triangular number nth term    return (3 * n * n +            3 * n + 2) / 2;} // Driver Codestatic public void Main (){ // For 3rd Centered// Triangular numberint n = 3;Console.WriteLine(Centered_Triangular_num(n)); // For 12th Centered// Triangular numbern = 12;Console.WriteLine(Centered_Triangular_num(n));}} // This code is contributed by akt_mit



Javascript



Output :

19
235

Time Complexity: O(1)
Auxiliary Space: O(1)

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