I got nerd sniped by this question, and I think I have a closed form formula. Obviously it needs a summation since the order/placement of the numbers matters.

I got nerd sniped by this question, and I think I have a closed form formula. Obviously it needs a summation since the order/placement of the numbers matters. The formula is 2^(# of questions - # terminating questions) + SUM[2^(terminiating question number - idx in terminating question list] where the SUM is over all the terms in the list given as input to the question_paths function for example: we take the example of question_paths(10,[1,5]), where the answer is 274. From the formula, we take 2^(10-2) + 2^(1-0) + 2^(5-1) which equals 274. similarly for question_paths(10,[6,8]), where the answer is 448. From the formula, we take 2^(10-2) + 2^(6-0) + 2^(8-1) which equals 448.