CSES - Odd lists

How many ways can you construct a list from the numbers 1 \dots n so that all sums of adjacent pairs are distinct and so that the first number is x?

You may assume that 1 \le n \le 8 and that 1 \le x \le n. The algorithm should be efficient in all these cases.

In a file oddlist.py, implement a function count that returns the desired count.

def count(n, x):
    # TODO

if __name__ == "__main__":
    print(count(1, 1)) # 1
    print(count(4, 2)) # 4
    print(count(8, 5)) # 830

Explanation: When n=4 and x=2, the answer is 4, because the lists are [2,1,3,4], [2,1,4,3], [2,4,1,3] and [2,4,3,1].

Odd lists