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 $[2,4,3,1]$.