# Program to check if N is a Centered Triangular Number

• Last Updated : 23 Jun, 2021

Given an integer N, the task is to check if it is a Centered triangular number or not.

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 . The first few Centered triangular numbers are 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, …

Examples:

Input: N = 4
Output: Yes
Input: 20
Output: No

Approach:

• The Kth Centered triangular number can be expressed as: • In order to check if the given number N can be expressed as a Centered triangular number or not, we need to check if gives an integer or not.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check// whether a given number is a// Centered triangular number or not#include using namespace std; // Function to check if the// number is a Centered// Triangular Numberbool isCenteredtriangular(int N){    float K = (-3               + sqrt(24 * N - 15))              / 6;     // Condition for K to be    // an integer    return (K - (int)K) == 0;} // Driver Codeint main(){    int N = 85;    if (isCenteredtriangular(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java implementation to check that// a number is a centered triangular// number or notimport java.lang.Math; class GFG{     // Function to check that the number// is a centered triangular numberpublic static boolean isCenteredTriangular(int N){    double K = (-3 + Math.sqrt(24 * N - 15)) / 6;     // Condition to check if the number    // is a centered triangular number    return (K - (int)K) == 0;} // Driver Codepublic static void main(String[] args){    int N = 85;     // Function call    if (isCenteredTriangular(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by ShubhamCoder

## Python3

 # Python3 implementation to check# whether a given number is a# Centered triangular number or notimport math # Function to check if the# number is a Centered# Triangular Numberdef isCenteredtriangular(N):         K = (-3 + math.sqrt(24 * N - 15)) / 6         # Condition for K to be    # an integer    if (K - int(K)) == 0:        return True             return False # Driver Code # Given NumberN = 85 # Function callif (isCenteredtriangular(N)):    print("Yes")else:    print("No") # This code is contributed by shubhamsingh10

## C#

 // C# implementation to check whether// a given number is a centered// triangular number or notusing System; class GFG{ // Function to check if the number// is a centered triangular numberstatic bool isCenteredtriangular(int N){    double K = (-3 + Math.Sqrt(24 * N - 15)) / 6;         // Condition for K to be    // an integer    return (K - (int)K) == 0;}     // Driver Codestatic public void Main (){    int N = 85;    if (isCenteredtriangular(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by shubhamsingh10

## Javascript

 

Output:

Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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