Via VBA,

Row\Col
A
B
C
D
E
1
States
 ABCDE ABCD
2
Start
 AAA B2: Input AAAA D2: Input
3
 AAB B3: =DecToBij(BijToDec(B2, B$1) + 1, B$1) AAAB D3: =DecToBij(BijToDec(D2, D$1) + 1, D$1)
4
 AAC AAAC
5
 AAD AAAD
6
 AAE AABA
7
 ABA AABB
8
 ABB AABC
9
 ABC AABD
10
 ABD AACA
11
 ABE AACB
12
 ACA AACC
13
 ACB AACD
14
 ACC AADA
15
 ACD AADB
16
 ACE AADC
17
 ADA AADD 


Function DecToBij(iNum As Long, sSym As String) As String
  ' shg 2014
  ' VBA or UDF
  
  ' Base sSym
  '   1  "1" (Tally)
  '   2  "12"
  '  10  "123456789A"
  '  26  "ABCDEFGHIJKLMNOPQRSTUVWXYZ" (Excel)
  
  ' Returns the bijective numeral for iNum using the digits in sSym
  
  ' https://en.wikipedia.org/wiki/Bijective_numeration
  ' https://en.wikipedia.org/wiki/Shortlex_order
  '

  If iNum > 0 Then DecToBij = DecToBij((iNum - 1) \ Len(sSym), sSym) & _
     Mid(sSym, ((iNum - 1) Mod Len(sSym)) + 1, 1)
End Function

Function BijToDec(sBij As String, sSym As String) As Long
  ' shg 2014
  ' VBA or UDF
  ' Returns the decimal value for the bijective numeral in sBij
  ' https://en.wikipedia.org/wiki/Bijective_numeration
  ' https://en.wikipedia.org/wiki/Shortlex_order

  If Len(sBij) Then BijToDec = InStr(sSym, Right(sBij, 1)) _
     + Len(sSym) * BijToDec(Left(sBij, Len(sBij) - 1), sSym)
End Function