The Samantha Clause
Santa Claus is only one of many members of the Claus family. Each of the members of the family has a unique name, based on the following rules.
- Each name can be obtained from the string SAMANTHA, by leaving out zero or more letters.
- Each name contains at least three letters.
- Each name contains at least one A.
- No name contains two or three consecutive As.
- No name contains more than three consecutive consonants.
For instance, valid names are SAM, SMAHA, MNTA, and ANH, but invalid are AM, SNT, SAATA, and AMNTH.
How many members does the Claus family have at most?