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# Centered Cube Number

A centered cube number is a number that can be expressed in the form (2n + 1)(n² + n + 1), where n is a non-negative integer. In other words, it is the product of an odd number and a centered square number. The centered square number for a given n is obtained by adding the numbers in a square pattern starting from the center and moving outward. The centered cube number sequence starts with 1 and continues as 9, 35, 91, 189, 341, and so on.

The provided code calculates and prints the first k centered cube numbers. It takes an input value k and iterates from 0 to k-1, calculating the centered cube number for each iteration using the formula mentioned above. The calculated number is then displayed on the screen.

## Example:

Let's take k = 5 as an example to understand how the code works.

For n = 0, the formula becomes: (2 * 0 + 1) * (0² + 0 + 1) = 1 * 1 = 1

For n = 1, the formula becomes: (2 * 1 + 1) * (1² + 1 + 1) = 3 * 3 = 9

For n = 2, the formula becomes: (2 * 2 + 1) * (2² + 2 + 1) = 5 * 7 = 35

For n = 3, the formula becomes: (2 * 3 + 1) * (3² + 3 + 1) = 7 * 13 = 91

For n = 4, the formula becomes: (2 * 4 + 1) * (4² + 4 + 1) = 9 * 21 = 189

Thus, the first 5 centered cube numbers are 1, 9, 35, 91, and 189.

## Algorithm:

1. Define a function centeredCubeNo that takes an integer k as input.
2. Initialize a variable ans to 0.
3. Iterate from n = 0 to n = k-1:
• Calculate the centered cube number using the formula: ans = (2 * n + 1) * (n² + n + 1).
• Print the calculated number.
4. End the function.
5. In the main function:
• Call the centeredCubeNo function with a specific value of k.
• Return 0 to indicate successful execution.

## Pseudocode:

``````
function centeredCubeNo(k):
ans = 0
for n = 0 to k-1:
ans = (2 * n + 1) * (n² + n + 1)
print ans
main():
centeredCubeNo(10)
return 0```
```

## Code Solution

Here given code implementation process.

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

void centeredCubeNo(int k)
{
int ans = 0;
// Print all initial k centered cube number
for (int n = 0; n < k; ++n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)
// Calculate nth centered number
ans = ((2 *n) + 1) *((n *n) + n + 1);
// Display calculate number
printf("  %d", ans);
}
}
int main()
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc
// Test
// k = 10
centeredCubeNo(10);
return 0;
}``````

#### Output

``  1  9  35  91  189  341  559  855  1241  1729``
``````// Java program for
//  Centered Cube Number
public class CubeNumber
{
public void centeredCubeNo(int k)
{
int ans = 0;
// Print all initial k centered cube number
for (int n = 0; n < k; ++n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
System.out.print(" " + ans);
}
}
public static void main(String[] args)
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc
// Test
// k = 10
}
}``````

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````// Include header file
#include <iostream>
using namespace std;
// C++ program for
//  Centered Cube Number
class CubeNumber
{
public: void centeredCubeNo(int k)
{
int ans = 0;
// Print all initial k centered cube number
for (int n = 0; n < k; ++n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 *n) + 1) *((n *n) + n + 1);

// Display calculate number
cout << " " << ans;
}
}
};
int main()
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````// Include namespace system
using System;
// Csharp program for
//  Centered Cube Number
public class CubeNumber
{
public void centeredCubeNo(int k)
{
int ans = 0;
// Print all initial k centered cube number
for (int n = 0; n < k; ++n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
Console.Write(" " + ans);
}
}
public static void Main(String[] args)
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````package main
import "fmt"
// Go program for
// Centered Cube Number

func centeredCubeNo(k int) {
var ans int = 0
// Print all initial k centered cube number
for n := 0 ; n < k ; n++ {
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1)

// Display calculate number
fmt.Print(" ", ans)
}
}
func main() {
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````<?php
// Php program for
//  Centered Cube Number
class CubeNumber
{
public	function centeredCubeNo(\$k)
{
\$ans = 0;
// Print all initial k centered cube number
for (\$n = 0; \$n < \$k; ++\$n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
\$ans = ((2 * \$n) + 1) * ((\$n * \$n) + \$n + 1);

// Display calculate number
echo(" ".\$ans);
}
}
}

function main()
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````// Node JS program for
//  Centered Cube Number
class CubeNumber
{
centeredCubeNo(k)
{
var ans = 0;
// Print all initial k centered cube number
for (var n = 0; n < k; ++n)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
process.stdout.write(" " + ans);
}
}
}

function main()
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc
// Test
// k = 10
}
main();``````

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````#  Python 3 program for
#   Centered Cube Number
class CubeNumber :
def centeredCubeNo(self, k) :
ans = 0
n = 0
#  Print all initial k centered cube number
while (n < k) :
#  Centered cube
#  formula =  (2n + 1)(n²+n+1)

#  Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1)

#  Display calculate number
print(" ", ans, end = "")
n += 1

def main() :
#  Centered cube numbers
#  --------------------------------------
#  1, 9, 35, 91, 189, 341, 559, 855, 1241,
#  1729, 2331, 3059, 3925, 4941, 6119 .. etc

#  Test
#  k = 10

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

#### Output

``  1  9  35  91  189  341  559  855  1241  1729``
``````#  Ruby program for
#   Centered Cube Number
class CubeNumber
def centeredCubeNo(k)
ans = 0
n = 0
#  Print all initial k centered cube number
while (n < k)
#  Centered cube
#  formula =  (2n + 1)(n²+n+1)

#  Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1)

#  Display calculate number
print(" ", ans)
n += 1
end

end

end

def main()
#  Centered cube numbers
#  --------------------------------------
#  1, 9, 35, 91, 189, 341, 559, 855, 1241,
#  1729, 2331, 3059, 3925, 4941, 6119 .. etc

#  Test
#  k = 10
end

main()``````

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````// Scala program for
//  Centered Cube Number
class CubeNumber()
{
def centeredCubeNo(k: Int): Unit = {
var ans: Int = 0;
var n: Int = 0;
// Print all initial k centered cube number
while (n < k)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
print(" " + ans);
n += 1;
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: CubeNumber = new CubeNumber();
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``
``````// Swift 4 program for
//  Centered Cube Number
class CubeNumber
{
func centeredCubeNo(_ k: Int)
{
var ans: Int = 0;
var n: Int = 0;
// Print all initial k centered cube number
while (n < k)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
print(" ", ans, terminator: "");
n += 1;
}
}
}
func main()
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

``  1  9  35  91  189  341  559  855  1241  1729``
``````// Kotlin program for
//  Centered Cube Number
class CubeNumber
{
fun centeredCubeNo(k: Int): Unit
{
var ans: Int ;
var n: Int = 0;
// Print all initial k centered cube number
while (n < k)
{
// Centered cube
// formula =  (2n + 1)(n²+n+1)

// Calculate nth centered number
ans = ((2 * n) + 1) * ((n * n) + n + 1);

// Display calculate number
print(" " + ans);
n += 1;
}
}
}
fun main(args: Array < String > ): Unit
{
// Centered cube numbers
// --------------------------------------
// 1, 9, 35, 91, 189, 341, 559, 855, 1241,
// 1729, 2331, 3059, 3925, 4941, 6119 .. etc

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

#### Output

`` 1 9 35 91 189 341 559 855 1241 1729``

## Output Explanation:

The code is executed with k = 10. It calculates and prints the first 10 centered cube numbers. The output is as follows:

1 9 35 91 189 341 559 855 1241 1729

These are the first 10 numbers in the centered cube number sequence.

## Time Complexity:

The time complexity of the code is O(k) because it iterates k times, and the calculations inside the loop have constant time complexity. The formula used to calculate the centered cube number can be computed in constant time for each iteration.

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