# Centered Dodecagonal Number

In mathematics, the centered dodecagonal number is a polygonal number that represents the number of points in a centered dodecagon. It can be calculated using the formula 5n² + 5n + 1, where n is the index of the centered dodecagonal number. The centered dodecagonal numbers are a sequence of integers that have unique properties and can be useful in various mathematical applications.

## Problem Statement

The problem is to write a program that generates and prints the first k centered dodecagonal numbers, where k is a user-defined input. The program should calculate each centered dodecagonal number using the formula mentioned above and display them in a formatted manner.

## Example

Let's consider the case where we want to find the first 10 centered dodecagonal numbers. Using the provided formula, we can calculate the centered dodecagonal numbers as follows:

• For n = 0: 5(0²) + 5(0) + 1 = 1
• For n = 1: 5(1²) + 5(1) + 1 = 11
• For n = 2: 5(2²) + 5(2) + 1 = 31
• For n = 3: 5(3²) + 5(3) + 1 = 61
• For n = 4: 5(4²) + 5(4) + 1 = 101
• For n = 5: 5(5²) + 5(5) + 1 = 151
• For n = 6: 5(6²) + 5(6) + 1 = 211
• For n = 7: 5(7²) + 5(7) + 1 = 281
• For n = 8: 5(8²) + 5(8) + 1 = 361
• For n = 9: 5(9²) + 5(9) + 1 = 451

Therefore, the first 10 centered dodecagonal numbers are 1, 11, 31, 61, 101, 151, 211, 281, 361, and 451.

## Algorithm

The algorithm to generate the first k centered dodecagonal numbers can be described as follows:

1. Start the program.
2. Define a function centeredDodecagonalNo(k) that takes an input parameter k.
3. Initialize a variable result to store the calculated centered dodecagonal number.
4. Use a loop to iterate from n = 0 to n < k:
• Inside the loop, calculate the centered dodecagonal number using the formula: result = 5n² + 5n + 1.
• Display the value of result.
5. End the loop.
6. End the function.
7. In the main program:
• Call the centeredDodecagonalNo(k) function with the desired value of k.
8. End the program.

## Pseudocode

``````
centeredDodecagonalNo(k):
result = 0
for n = 0 to n < k:
result = 5 * n^2 + 5 * n + 1
display result
end for
end function

main:
centeredDodecagonalNo(k)
end main
```
```

## Code Solution

Here given code implementation process.

``````// C Program for
// Centered Dodecagonal Number
#include <stdio.h>

void centeredDodecagonalNo(int k)
{
int result = 0;
// Print all initial k centered Dodecagonal number
for (int n = 0; n < k; ++n)
{
// Centered dodecagonal formula =  5n²+5n+ 1
result = ((5 *(n *n) + (5 *n) + 1));
// Display value
printf("  %d", result);
}
}
int main()
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc
// Test
// k  = 10
centeredDodecagonalNo(10);
return 0;
}``````

#### Output

``  1  11  31  61  101  151  211  281  361  451``
``````// Java program for
// Centered Dodecagonal Number
public class DodecagonalNumber
{
public void centeredDodecagonalNo(int k)
{
int result = 0;
// Print all initial k centered dodecagonal number
for (int n = 0; n < k; ++n)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
System.out.print(" " + result);
}
}
public static void main(String[] args)
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
}
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Centered Dodecagonal Number

class DodecagonalNumber
{
public: void centeredDodecagonalNo(int k)
{
int result = 0;
// Print all initial k centered dodecagonal number
for (int n = 0; n < k; ++n)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 *(n *n) + (5 *n) + 1));

// Display calculated result
cout << " " << result;
}
}
};
int main()
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
return 0;
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````// Include namespace system
using System;
// Csharp program for
// Centered Dodecagonal Number
public class DodecagonalNumber
{
public void centeredDodecagonalNo(int k)
{
int result = 0;
// Print all initial k centered dodecagonal number
for (int n = 0; n < k; ++n)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
Console.Write(" " + result);
}
}
public static void Main(String[] args)
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
}
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````package main
import "fmt"
// Go program for
// Centered Dodecagonal Number

func centeredDodecagonalNo(k int) {
var result int = 0
// Print all initial k centered dodecagonal number
for n := 0 ; n < k ; n++ {
// Centered dodecagonal
// formula =  5n²+5n+ 1
// Calculate result
result = ((5 * (n * n) + (5 * n) + 1))
// Display calculated result
fmt.Print(" ", result)
}
}
func main() {
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
centeredDodecagonalNo(10)
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````<?php
// Php program for
// Centered Dodecagonal Number
class DodecagonalNumber
{
public	function centeredDodecagonalNo(\$k)
{
\$result = 0;
// Print all initial k centered dodecagonal number
for (\$n = 0; \$n < \$k; ++\$n)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
\$result = ((5 * (\$n * \$n) + (5 * \$n) + 1));

// Display calculated result
echo(" ".\$result);
}
}
}

function main()
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc
// Test
// k  = 10
}
main();``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````// Node JS program for
// Centered Dodecagonal Number
class DodecagonalNumber
{
centeredDodecagonalNo(k)
{
var result = 0;
// Print all initial k centered dodecagonal number
for (var n = 0; n < k; ++n)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
process.stdout.write(" " + result);
}
}
}

function main()
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
}
main();``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````#  Python 3 program for
#  Centered Dodecagonal Number
class DodecagonalNumber :
def centeredDodecagonalNo(self, k) :
result = 0
n = 0
#  Print all initial k centered dodecagonal number
while (n < k) :
#  Centered dodecagonal
#  formula =  5n²+5n+ 1

#  Calculate result
result = ((5 * (n * n) + (5 * n) + 1))

#  Display calculated result
print(" ", result, end = "")
n += 1

def main() :
#  Centered Dodecagonal numbers
#  --------------------------------------
#  1, 11, 31, 61, 101, 151, 211, 281, 361,
#  451, 551, 661, 781, 9119 .. etc

#  Test
#  k  = 10

if __name__ == "__main__": main()``````

#### Output

``  1  11  31  61  101  151  211  281  361  451``
``````#  Ruby program for
#  Centered Dodecagonal Number
class DodecagonalNumber
def centeredDodecagonalNo(k)
result = 0
n = 0
#  Print all initial k centered dodecagonal number
while (n < k)
#  Centered dodecagonal
#  formula =  5n²+5n+ 1

#  Calculate result
result = ((5 * (n * n) + (5 * n) + 1))

#  Display calculated result
print(" ", result)
n += 1
end

end

end

def main()
#  Centered Dodecagonal numbers
#  --------------------------------------
#  1, 11, 31, 61, 101, 151, 211, 281, 361,
#  451, 551, 661, 781, 9119 .. etc
#  Test
#  k  = 10
end

main()``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````// Scala program for
// Centered Dodecagonal Number
class DodecagonalNumber()
{
def centeredDodecagonalNo(k: Int): Unit = {
var result: Int = 0;
var n: Int = 0;
// Print all initial k centered dodecagonal number
while (n < k)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
print(" " + result);
n += 1;
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: DodecagonalNumber = new DodecagonalNumber();
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc
// Test
// k  = 10
}
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``
``````// Swift 4 program for
// Centered Dodecagonal Number
class DodecagonalNumber
{
func centeredDodecagonalNo(_ k: Int)
{
var result: Int = 0;
var n: Int = 0;
// Print all initial k centered dodecagonal number
while (n < k)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
print(" ", result, terminator: "");
n += 1;
}
}
}
func main()
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc
// Test
// k  = 10
}
main();``````

#### Output

``  1  11  31  61  101  151  211  281  361  451``
``````// Kotlin program for
// Centered Dodecagonal Number
class DodecagonalNumber
{
fun centeredDodecagonalNo(k: Int): Unit
{
var result: Int ;
var n: Int = 0;
// Print all initial k centered dodecagonal number
while (n < k)
{
// Centered dodecagonal
// formula =  5n²+5n+ 1

// Calculate result
result = ((5 * (n * n) + (5 * n) + 1));

// Display calculated result
print(" " + result);
n += 1;
}
}
}
fun main(args: Array < String > ): Unit
{
// Centered Dodecagonal numbers
// --------------------------------------
// 1, 11, 31, 61, 101, 151, 211, 281, 361,
// 451, 551, 661, 781, 9119 .. etc

// Test
// k  = 10
}``````

#### Output

`` 1 11 31 61 101 151 211 281 361 451``

## Result

When we run the provided code with the input k = 10, it will generate and display the first 10 centered dodecagonal numbers: 1, 11, 31, 61, 101, 151, 211, 281, 361, and 451.

The time complexity of this code is O(k) because the loop runs k times, where k is the desired number of centered dodecagonal numbers to be generated. The calculations inside the loop have constant time complexity, so they do not affect the overall time complexity.

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