Find the number of non-decreasing sequences of 75 integers from 1 to 75 which have same mean as the median.

If n = 1 (instead of 75), the number of such sequences = 1

If n = 3, the number of such sequences = 4

If n = 5, the number of such sequences = 16 (I think)

So, I'm wondering if the number of sequences is 4^((n-1)/2).

For n = 75, that would be 4^37

No proof, and I'm even betting this is not the case, but I'll put it out there while I'm doing more exploration.