# Generate an alternate odd-even sequence having sum of all consecutive pairs as a perfect square

Given an integer N, the task is to print a sequence of length N consisting of alternate odd and even numbers in increasing order such that the sum of any two consecutive terms is a perfect square.

Examples:

Input: N = 4
Output: 1 8 17 32
Explanation:
1 + 8 = 9 = 32
8 + 17 = 25 = 52
17 + 32 = 49 = 72

Input: N = 2
Output: 1 8

Approach: The given problem can be solved based on the observation from the above examples, that for an integer N, sequence will be of the form 1, 8, 17, 32, 49 and so on. Therefore, the Nth term can be calculated by the following equation: Therefore, to solve the problem, traverse the range [1, N] to calculate and print every term of the sequence using the above formula.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to print the` `// required sequence` `void` `findNumbers(``int` `n)` `{` `    ``int` `i = 0;` `    ``while` `(i <= n) {`   `        ``// Print ith odd number` `        ``cout << 2 * i * i + 4 * i` `                    ``+ 1 + i % 2` `             ``<< ``" "``;` `        ``i++;` `    ``}` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `n = 6;` `    ``findNumbers(n);` `}`

## Java

 `// Java program to implement ` `// the above approach ` `import` `java.util.*;`   `class` `GFG{` `    `  `// Function to print the ` `// required sequence ` `static` `void` `findNumbers(``int` `n) ` `{ ` `    ``int` `i = ``0``; ` `    ``while` `(i <= n)` `    ``{ `   `        ``// Print ith odd number ` `        ``System.out.print(``2` `* i * i + ``4` `* i + ` `                         ``1` `+ i % ``2` `+ ``" "``); ` `        ``i++; ` `    ``} ` `} `   `// Driver code` `public` `static` `void` `main (String[] args)` `{` `    ``int` `n = ``6``;` `    `  `    ``// Function call` `    ``findNumbers(n); ` `}` `}`   `// This code is contributed by offbeat`

## Python3

 `# Python3 program to implement` `# the above approach` ` `  `# Function to prthe` `# required sequence` `def` `findNumbers(n):` `    `  `    ``i ``=` `0` `    ``while` `(i <``=` `n):` ` `  `        ``# Print ith odd number` `        ``print``(``2` `*` `i ``*` `i ``+` `4` `*` `i ``+` `              ``1` `+` `i ``%` `2``, end ``=` `" "``)` `              `  `        ``i ``+``=` `1` `    `  `# Driver Code` `n ``=` `6`   `findNumbers(n)`   `# This code is contributed by sanjoy_62`

## C#

 `// C# program to implement ` `// the above approach ` `using` `System;` ` `  `class` `GFG{` `     `  `// Function to print the ` `// required sequence ` `static` `void` `findNumbers(``int` `n) ` `{ ` `    ``int` `i = 0; ` `    ``while` `(i <= n)` `    ``{ ` `        `  `        ``// Print ith odd number ` `        ``Console.Write(2 * i * i + 4 * i + ` `                      ``1 + i % 2 + ``" "``); `   `        ``i++; ` `    ``} ` `} ` ` `  `// Driver code` `public` `static` `void` `Main ()` `{` `    ``int` `n = 6;` `     `  `    ``// Function call` `    ``findNumbers(n); ` `}` `}` ` `  `// This code is contributed by sanjoy_62`

Output:

```1 8 17 32 49 72 97

```

Time Complexity: O(N)
Auxiliary Space: O(1)

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Improved By : offbeat, sanjoy_62

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