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Code Number

# Octahedral number

An octahedral number is a figurate number that represents the number of spheres in an octahedron made by stacking layers of spheres. It can also be visualized as the sum of the first n triangular numbers. The formula for finding the nth octahedral number is n(2n² + 1) / 3.

## Problem Statement

The task is to generate the first k octahedral numbers using the given formula and display the results.

### Example

Let's take k = 5 as an example to understand the process of generating octahedral numbers.

1. For n = 1: Octahedral number = (1 * (2 * (1 * 1) + 1)) / 3 = 1
2. For n = 2: Octahedral number = (2 * (2 * (2 * 2) + 1)) / 3 = 6
3. For n = 3: Octahedral number = (3 * (2 * (3 * 3) + 1)) / 3 = 19
4. For n = 4: Octahedral number = (4 * (2 * (4 * 4) + 1)) / 3 = 44
5. For n = 5: Octahedral number = (5 * (2 * (5 * 5) + 1)) / 3 = 85

## Pseudocode

1. Start with a function to calculate and display the first k octahedral numbers.
2. Inside the function, use a loop to iterate from n = 1 to n = k.
3. For each value of n, apply the octahedral number formula (n(2n² + 1) / 3) to find the result.
4. Print the calculated result for each value of n.

## Algorithm

``````FUNCTION octahedralNo(k):
FOR n = 1 to k:
result = (n * (2 * (n * n) + 1)) / 3
PRINT result
END FOR
END FUNCTION

FUNCTION main():
SET k = 10
CALL octahedralNo(k)
END FUNCTION
``````

## Code Solution

Here given code implementation process.

``````// C Program for
// Octahedral number
#include <stdio.h>

void octahedralNo(int k)
{
// Print all initial k octahedral number
for (int n = 1; n <= k; ++n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
int result = (n *(2 *(n *n) + 1)) / 3;

// Display calculated result
printf("  %d", result);
}
}
int main()
{
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

// k = 10
octahedralNo(10);
return 0;
}``````

#### Output

``  1  6  19  44  85  146  231  344  489  670``
``````// Java program for
// Octahedral number
public class OctahedralNumber
{
public void octahedralNo(int k)
{
// Print all initial k octahedral number
for (int n = 1; n <= k; ++n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
int result = (n * (2 * (n * n) + 1)) / 3;

// Display calculated result
System.out.print(" " + result);
}
}
public static void main(String[] args)
{
OctahedralNumber task = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

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

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Octahedral number

class OctahedralNumber
{
public: void octahedralNo(int k)
{
// Print all initial k octahedral number
for (int n = 1; n <= k; ++n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
int result = (n *(2 *(n *n) + 1)) / 3;

// Display calculated result
cout << " " << result;
}
}
};
int main()
{
OctahedralNumber *task = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

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

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````package main
import "fmt"
// Go program for
// Octahedral number

func octahedralNo(k int) {
// Print all initial k octahedral number
for n := 1 ; n <= k ; n++ {
// Formula
//   n(2n²+1)
//  —————————
//      3
// Calculate nth octahedral number
var result int = (n * (2 * (n * n) + 1)) / 3

// Display calculated result
fmt.Print(" ", result)
}
}
func main() {

//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

// k = 10
octahedralNo(10)
}``````

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````// Include namespace system
using System;

// Csharp program for
// Octahedral number

public class OctahedralNumber
{
public void octahedralNo(int k)
{
// Print all initial k octahedral number
for (int n = 1; n <= k; ++n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
int result = (n * (2 * (n * n) + 1)) / 3;

// Display calculated result
Console.Write(" " + result);
}
}
public static void Main(String[] args)
{
OctahedralNumber task = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

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

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````<?php
// Php program for
// Octahedral number
class OctahedralNumber
{
public	function octahedralNo(\$k)
{
// Print all initial k octahedral number
for (\$n = 1; \$n <= \$k; ++\$n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
\$result = (int)((\$n * (2 * (\$n * \$n) + 1)) / 3);

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

function main()
{
\$task = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.
// k = 10
}
main();``````

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````// Node JS program for
// Octahedral number
class OctahedralNumber
{
octahedralNo(k)
{
// Print all initial k octahedral number
for (var n = 1; n <= k; ++n)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
var result = parseInt((n * (2 * (n * n) + 1)) / 3);

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

function main()
{
var task = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

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

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````#  Python 3 program for
#  Octahedral number
class OctahedralNumber :
def octahedralNo(self, k) :
n = 1
#  Print all initial k octahedral number
while (n <= k) :
#  Formula
#    n(2n²+1)
#   —————————
#      3

#  Calculate nth octahedral number
result = int((n * (2 * (n * n) + 1)) / 3)

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

def main() :
#   Octahedral number are
#  —————————————————————————————————————————————
#   1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
#   891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
#   4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
#   13131, 14644, 16269, 18010, 19871, 21856, 23969,
#   26214, 28595, 31116, 33781, 36594, 39559 etc.

#  k = 10

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

#### Output

``  1  6  19  44  85  146  231  344  489  670``
``````#  Ruby program for
#  Octahedral number
class OctahedralNumber
def octahedralNo(k)
n = 1
#  Print all initial k octahedral number
while (n <= k)
#  Formula
#    n(2n²+1)
#   —————————
#      3

#  Calculate nth octahedral number
result = (n * (2 * (n * n) + 1)) / 3

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

end

end

def main()
#   Octahedral number are
#  —————————————————————————————————————————————
#   1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
#   891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
#   4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
#   13131, 14644, 16269, 18010, 19871, 21856, 23969,
#   26214, 28595, 31116, 33781, 36594, 39559 etc.
#  k = 10
end

main()``````

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````// Scala program for
// Octahedral number
class OctahedralNumber()
{
def octahedralNo(k: Int): Unit = {
var n: Int = 1;
// Print all initial k octahedral number
while (n <= k)
{
// Formula

//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
var result: Int = (n * (2 * (n * n) + 1)) / 3;

// Display calculated result
print(" " + result);
n += 1;
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: OctahedralNumber = new OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.

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

#### Output

`` 1 6 19 44 85 146 231 344 489 670``
``````// Swift 4 program for
// Octahedral number
class OctahedralNumber
{
func octahedralNo(_ k: Int)
{
var n: Int = 1;
// Print all initial k octahedral number
while (n <= k)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
let result: Int = (n * (2 * (n * n) + 1)) / 3;

// Display calculated result
print(" ", result, terminator: "");

n += 1;
}
}
}
func main()
{
let task: OctahedralNumber = OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.
// k = 10
}
main();``````

#### Output

``  1  6  19  44  85  146  231  344  489  670``
``````// Kotlin program for
// Octahedral number
class OctahedralNumber
{
fun octahedralNo(k: Int): Unit
{
var n: Int = 1;
// Print all initial k octahedral number
while (n <= k)
{
// Formula
//   n(2n²+1)
//  —————————
//     3

// Calculate nth octahedral number
val result: Int = (n * (2 * (n * n) + 1)) / 3;

// Display calculated result
print(" " + result);
n += 1;
}
}
}
fun main(args: Array < String > ): Unit
{
val task: OctahedralNumber = OctahedralNumber();
//  Octahedral number are
// —————————————————————————————————————————————
//  1, 6, 19, 44, 85, 146, 231, 344, 489, 670,
//  891, 1156, 1469, 1834, 2255, 2736, 3281, 3894,
//  4579, 5340, 6181, 7106, 8119, 9224, 10425, 11726,
//  13131, 14644, 16269, 18010, 19871, 21856, 23969,
//  26214, 28595, 31116, 33781, 36594, 39559 etc.
// k = 10
}``````

#### Output

`` 1 6 19 44 85 146 231 344 489 670``

## Resultant Output Explanation

For k = 10, the first 10 octahedral numbers will be generated and displayed using the function octahedralNo(k). The output will be: 1 6 19 44 85 146 231 344 489 670

## Time Complexity

The time complexity of this algorithm is O(k), where k is the number of octahedral numbers to be generated. Since we are using a loop to iterate from n = 1 to n = k and performing constant time operations within each iteration, the overall time complexity is directly proportional to k.

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