Increment alphanumeric sequence

I am trying to create a method using the APEX language (Salesforce) that will increment a 3-digit alphanumeric sequence. Java is the closest to the APEX language, but it also share similarities with C#. I was hoping a JAVA or C# guru could point me in the right direction with the method to get the sequencing correct.

The sequence is as follows:

001 -> 999 (go thru all numeric)
A01 -> A99 (start alphanumeric)
B01 -> B99
.
.
.
Z01 -> Z99
AA1 -> AA9
BB1 -> BB9 
.
.
. 
ZZ1 -> ZZ9 (all alphanumeric utilized)
AAA -> AAZ (start all alpha)
BAA -> BAZ
.
.
.
ZAA -> ZZA
ZZB -> ZZZ (all alpha completed)
reset
001 (begin cycling thru sequence again)

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I was trying to modify the following method to make it work, but am not having much luck

	public enum EMode {
    	AlphaNumeric, Alpha, Numeric
	}

	public String Increment(string text, EMode mode) {
		String retval = '';
    	String[] textArr = text.split('');
		textArr.remove(0);
		
    	// Add legal characters
    	List<String> characters = new List<String>();

    	if (mode == EMode.AlphaNumeric || mode == EMode.Numeric) {
        	for(Integer i = 0; i <= 9; i++) {
            	characters.add(String.valueOf(i));
        	}
    	}

    	if (mode == EMode.AlphaNumeric || mode == EMode.Alpha) {
        	for(String s = 'A'; s <= 'Z'; s++)
            	characters.add(s);
    	}

    	// Loop from end to beginning
    	for (Integer i = textArr.length - 1; i >= 0; i--)
    	{
        	if (textArr[i] == characters.Last())
        	{
            	//textArr[i] = characters.First();
            	retval = characters.First();
        	}
        	else
        	{
            	//textArr[i] = characters[characters.IndexOf(textArr[i]) + 1];
            	retval = characters[characters.IndexOf(textArr[i]) + 1];
            	break;
        	}
    	}
    	//return new string(textArr);
    	return retval;
	}

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Unfortunately, APEX has limitations on the available libraries, so I'm working within the confines of the language and trying to use the available string methods: Apex String Methods

There is probably an easier way to accomplish the sequence perhaps using maps? Any and all suggestions are welcome.

Thanks in advance for any help.