Why Your Game Instantly Died (And How to Overhaul Action Now!)

Game crashes are up, and players are finally asking why their sessions end in seconds.

Game crashes are up, and players are finally asking why their sessions end in seconds.
Let $ a_n $ be total valid sequences of length $ n $.
Let $ b_n $ be sequences of length $ n $ ending in H, and $ c_n $ those ending in L or M. Then:
$ a_2 = 2a_1 + 2a_0 $? But $ a_0 = 1 $ (empty sequence)
$ a_3 = 2a_2 + 2a_1 = 2(8) + 2(3) = 16 + 6 = 22 $
$ a_4 = 2a_3 + 2a_2 = 2(22) + 2(8) = 44 + 16 = 60 $
$ a_5 = 2a_4 + 2a_3 = 2(60) + 2(22) = 120 + 44 = 164 $
So, there are 164 valid sequences of 5 hours with no two consecutive high readings.
Question: A virologist has 3 types of synthetic RNA sequences: 4 copies of type A, 3 of type B, and 2 of type C. If she runs them in a sequence over 9 days, one per day, how many distinct sequences can she create?
Solution: We are arranging 9 RNA segments where 4 are identical of type A, 3 of type B, and 2 of type C. The number of distinct permutations is:
Question: A primatologist records 6 social interactions among a troop, categorized as 3 grooming events, 2 play events, and 1 aggression event. If the sequence of behaviors is analyzed and events of the same type are indistinguishable, how many distinct behavioral sequences are possible?