Every 9-statement sequence ("9SS") can be converted into a 10SS sequence by appending a true statement. Every 8SS can be converted into a 10SS by appending first a true statement, and then a false statement.
(The reciprocal processes are also valid; if a 10SS ends in a true statement, remove it and you'll get a 9SS, and if the 10SS ends in a false statement, remove the last two statements, and you'll get a 8SS.)
Thus, the number of 10SS= the number of 9SS+ the number of 8SS (let's write 10SS=9SS+8SS) and recursively, in a Fibonacci way, 9SS=8SS+7SS, 8SS=7SS+6SS... Since 1SS=2 and 2SS=3, 10SS=144.