In game theory, the average branching factor refers to the average number
of legal moves available to a player at each turn. In chess, the average
branching factor is about 35.
If Jules wants to write a chess simulation program that represents every
possible sequence of moves in a game that lasts n moves, the following
function approximates the number of distinct sequences s(n) he would
simulate.
s(n) = 35n
How many times greater does the number of sequences become each time
the game lasts 2 moves longer?