Holiday Contest 2025 - Guts Round - Set 7 Problem 2

A piece of chalk has a durability of 40 units. It takes 1 unit of durability to draw the letter A and 2 units of durability to draw the letter B. A sequence of A and Bs is made where no A can appear more than 2 times in a row and no B can appear more than 1 time in a row. How many different sequences of exactly length 30 are possible to draw with one piece of chalk.