Centered square numbers
In mathematics, centered square numbers are a sequence of numbers obtained by squaring the positive integers and
adding consecutive odd numbers to them. These numbers are called "centered" because they can be visually represented
as a square with a central dot surrounded by layers of concentric squares. The formula to calculate centered square
numbers is (n^2) + ((n - 1)^2), where n represents the position in the sequence.
Let's take an example to understand this concept. Suppose we want to find the first 5 centered square numbers. We start with the number 1, which is obtained by squaring 1. The next number is calculated by squaring 2 (4) and adding the previous square, which is 0. So, the second centered square number is 4 + 0 = 4. Following the same pattern, we can calculate the third, fourth, and fifth centered square numbers as 9, 16, and 25, respectively.
Here's the algorithm to generate the first k centered square numbers:
centeredSquareNo(k):
for n = 1 to k:
result = (n^2) + ((n - 1)^2)
print result
Code Solution
Here given code implementation process.
// C Program for
// Centered square numbers
#include <stdio.h>
void centeredSquareNo(int k)
{
// Print all initial k centered square number
for (int n = 1; n <= k; ++n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
int result = ((n *n) + ((n - 1) *(n - 1)));
// Display calculated result
printf(" %d", result);
}
}
int main()
{
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
centeredSquareNo(10);
return 0;
}Output
1 5 13 25 41 61 85 113 145 181// Java program for
// Centered square numbers
public class SquareNumber
{
public void centeredSquareNo(int k)
{
// Print all initial k centered square number
for (int n = 1; n <= k; ++n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
int result = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
System.out.print(" " + result);
}
}
public static void main(String[] args)
{
SquareNumber task = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}
}Output
1 5 13 25 41 61 85 113 145 181// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Centered square numbers
class SquareNumber
{
public: void centeredSquareNo(int k)
{
// Print all initial k centered square number
for (int n = 1; n <= k; ++n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
int result = ((n *n) + ((n - 1) *(n - 1)));
// Display calculated result
cout << " " << result;
}
}
};
int main()
{
SquareNumber *task = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task->centeredSquareNo(10);
return 0;
}Output
1 5 13 25 41 61 85 113 145 181// Include namespace system
using System;
// Csharp program for
// Centered square numbers
public class SquareNumber
{
public void centeredSquareNo(int k)
{
// Print all initial k centered square number
for (int n = 1; n <= k; ++n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
int result = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
Console.Write(" " + result);
}
}
public static void Main(String[] args)
{
SquareNumber task = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}
}Output
1 5 13 25 41 61 85 113 145 181package main
import "fmt"
// Go program for
// Centered square numbers
func centeredSquareNo(k int) {
// Print all initial k centered square number
for n := 1 ; n <= k ; n++ {
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
var result int = ((n * n) + ((n - 1) * (n - 1)))
// Display calculated result
fmt.Print(" ", result)
}
}
func main() {
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
centeredSquareNo(10)
}Output
1 5 13 25 41 61 85 113 145 181<?php
// Php program for
// Centered square numbers
class SquareNumber
{
public function centeredSquareNo($k)
{
// Print all initial k centered square number
for ($n = 1; $n <= $k; ++$n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
$result = (($n * $n) + (($n - 1) * ($n - 1)));
// Display calculated result
echo(" ".$result);
}
}
}
function main()
{
$task = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
$task->centeredSquareNo(10);
}
main();Output
1 5 13 25 41 61 85 113 145 181// Node JS program for
// Centered square numbers
class SquareNumber
{
centeredSquareNo(k)
{
// Print all initial k centered square number
for (var n = 1; n <= k; ++n)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
var result = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
process.stdout.write(" " + result);
}
}
}
function main()
{
var task = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}
main();Output
1 5 13 25 41 61 85 113 145 181# Python 3 program for
# Centered square numbers
class SquareNumber :
def centeredSquareNo(self, k) :
n = 1
# Print all initial k centered square number
while (n <= k) :
# Centered square
# formula = (n)² + (n-1)²
# CalculatedCentered square numbers
result = ((n * n) + ((n - 1) * (n - 1)))
# Display calculated result
print(" ", result, end = "")
n += 1
def main() :
task = SquareNumber()
# Centered square numbers
# --------------------------------------
# 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
# 265, 313, 365, 421, 481, 545, 613, 685, 761,
# 841, 925, 1013, 1105, 1201, 1301, 1405,
# 1513, 1625, 1741, 1861, 1985, 2113, 2245,
# 2381, 2521, 2665, 2813, 2965, 3121, 3281,
# 3445, 3613, 3785, 3961, 4141 .. etc
# Test
# k = 10
task.centeredSquareNo(10)
if __name__ == "__main__": main()Output
1 5 13 25 41 61 85 113 145 181# Ruby program for
# Centered square numbers
class SquareNumber
def centeredSquareNo(k)
n = 1
# Print all initial k centered square number
while (n <= k)
# Centered square
# formula = (n)² + (n-1)²
# CalculatedCentered square numbers
result = ((n * n) + ((n - 1) * (n - 1)))
# Display calculated result
print(" ", result)
n += 1
end
end
end
def main()
task = SquareNumber.new()
# Centered square numbers
# --------------------------------------
# 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
# 265, 313, 365, 421, 481, 545, 613, 685, 761,
# 841, 925, 1013, 1105, 1201, 1301, 1405,
# 1513, 1625, 1741, 1861, 1985, 2113, 2245,
# 2381, 2521, 2665, 2813, 2965, 3121, 3281,
# 3445, 3613, 3785, 3961, 4141 .. etc
# Test
# k = 10
task.centeredSquareNo(10)
end
main()Output
1 5 13 25 41 61 85 113 145 181// Scala program for
// Centered square numbers
class SquareNumber()
{
def centeredSquareNo(k: Int): Unit = {
var n: Int = 1;
// Print all initial k centered square number
while (n <= k)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
var result: Int = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
print(" " + result);
n += 1;
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: SquareNumber = new SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}
}Output
1 5 13 25 41 61 85 113 145 181// Swift 4 program for
// Centered square numbers
class SquareNumber
{
func centeredSquareNo(_ k: Int)
{
var n: Int = 1;
// Print all initial k centered square number
while (n <= k)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
let result: Int = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
print(" ", result, terminator: "");
n += 1;
}
}
}
func main()
{
let task: SquareNumber = SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}
main();Output
1 5 13 25 41 61 85 113 145 181// Kotlin program for
// Centered square numbers
class SquareNumber
{
fun centeredSquareNo(k: Int): Unit
{
var n: Int = 1;
// Print all initial k centered square number
while (n <= k)
{
// Centered square
// formula = (n)² + (n-1)²
// CalculatedCentered square numbers
val result: Int = ((n * n) + ((n - 1) * (n - 1)));
// Display calculated result
print(" " + result);
n += 1;
}
}
}
fun main(args: Array < String > ): Unit
{
val task: SquareNumber = SquareNumber();
// Centered square numbers
// --------------------------------------
// 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221,
// 265, 313, 365, 421, 481, 545, 613, 685, 761,
// 841, 925, 1013, 1105, 1201, 1301, 1405,
// 1513, 1625, 1741, 1861, 1985, 2113, 2245,
// 2381, 2521, 2665, 2813, 2965, 3121, 3281,
// 3445, 3613, 3785, 3961, 4141 .. etc
// Test
// k = 10
task.centeredSquareNo(10);
}Output
1 5 13 25 41 61 85 113 145 181Time complexity
The time complexity of the algorithm is O(k), as it performs a constant amount of work for each value
from 1 to k. The space complexity is constant as well, as it only requires a single variable to store
the calculated result.
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