PROBLEM $2$: $(25$ points$)$

You will write a recursive function in C to print the pattern that is shown in the examples below.

You will also write a main program to test your function. Examples are given of the output

on your screen for two values of number of rows. Your program must work for all values of

number of rows $>0$ and $20.$ While verifying your value of the number of rows you may need to print any one of the following error messages or prompts.

Enter the number of rows:ERROR: The number of rows is out of range.

ERROR: Too many tries attempting to read the number of rows for the pattern.

HINT: the numbers in each row are determined using the same pattern, for example for

the longest row in the second example:

Second number $=$ first number $+2$

Third number $=$ second number $+3$

Fourth number $=$ Third number $+4$

Fifth number $=$ fourth number $-4$

Sixth number $=$ fifth number $-3$

Seventh number $=$ sixth number $-2$

If you wish you can write an iterative function to print one line of one of these patterns.

The line printed will contain an odd number $P$ of integers following the pattern given in the

hint above. You may also elect to include the iterative code to print the single line of the

pattern within your recursive function to print the entire pattern.

You will write a recursive function to print the entire pattern line by line. Recursion is with

respect to the lines of the pattern not numbers in each line of the pattern.

When you look at the examples you will see that the pattern always has an odd number of

lines. If you ask for an even number of lines, Neven, the pattern will be the same as if you

asked for the pattern for Neven$-1$ lines.

You will write a main program. The main program will read the number of rows. You may

assume the user enters an integer. If the integer entered is out of range re$-$prompt, reread

and re$-$test the value supplied. You should prompt a maximum of $5$ times, terminating your

program if no valid value of the number of rows is read in $5$ tries.

You will call your recursive function to print the pattern