# Centered tetrahedral number

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++

`// C++ Program to find nth ` `// Centered tetrahedral number ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find centered ` `// Centered tetrahedral number ` `int` `centeredTetrahedralNumber(` `int` `n) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// Centered tetrahedral number ` ` ` `// and return it into main function. ` ` ` `return` `(2 * n + 1) * (n * n + n + 3) / 3; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 6; ` ` ` ` ` `cout << centeredTetrahedralNumber(n); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find nth Centered ` `// tetrahedral number ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find centered ` ` ` `// Centered tetrahedral number ` ` ` `static` `int` `centeredTetrahedralNumber(` `int` `n) ` ` ` `{ ` ` ` ` ` `// Formula to calculate nth ` ` ` `// Centered tetrahedral number ` ` ` `// and return it into main function. ` ` ` `return` `(` `2` `* n + ` `1` `) * (n * n + n + ` `3` `) / ` `3` `; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` ` ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `n = ` `6` `; ` ` ` ` ` `System.out.println( ` ` ` `centeredTetrahedralNumber(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## Python3

`# Python program to find nth ` `# Centered tetrahedral number ` ` ` `# Function to calculate ` `# Centered tetrahedral number ` ` ` `def` `centeredTetrahedralNumber(n): ` ` ` ` ` `# Formula to calculate nth ` ` ` `# Centered tetrahedral number ` ` ` `# and return it into main function ` ` ` ` ` `return` `(` `2` `*` `n ` `+` `1` `) ` `*` `(n ` `*` `n ` `+` `n ` `+` `3` `) ` `/` `/` `3` ` ` `# Driver Code ` `n ` `=` `6` `print` `(centeredTetrahedralNumber(n)) ` ` ` `# This code is contributed by ajit ` |

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## C#

`// C# Program to find nth Centered ` `// tetrahedral number ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find centered ` ` ` `// Centered tetrahedral number ` ` ` `static` `int` `centeredTetrahedralNumber(` `int` `n) ` ` ` `{ ` ` ` ` ` `// Formula to calculate nth ` ` ` `// Centered tetrahedral number ` ` ` `// and return it into main function. ` ` ` `return` `(2 * n + 1) * (n * n + n + 3) / 3; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` ` ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `n = 6; ` ` ` ` ` `Console.WriteLine( ` ` ` `centeredTetrahedralNumber(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## PHP

`<?php ` `// PHP Program to find nth ` `// Centered tetrahedral number ` ` ` `// Function to find centered ` `// Centered tetrahedral number ` `function` `centeredTetrahedralNumber(` `$n` `) ` `{ ` ` ` `// Formula to calculate nth ` ` ` `// Centered tetrahedral number ` ` ` `// and return it into main function. ` ` ` `return` `(2 * ` `$n` `+ 1) * ` ` ` `(` `$n` `* ` `$n` `+ ` `$n` `+ 3) / 3; ` `} ` ` ` `// Driver Code ` `$n` `= 6; ` ` ` `echo` `centeredTetrahedralNumber(` `$n` `); ` ` ` `// This code is contributed by anuj_67. ` `?> ` |

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**Output :**

195

## Recommended Posts:

- Centered heptagonal number
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- Centered Pentadecagonal Number
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- Centered Hexadecagonal Number
- Centered Dodecagonal Number
- Centered triangular number
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