Let $\displaystyle n=2m+1$, an odd natural number.

The $\displaystyle 10^n$ numbers with $\displaystyle n$ digits are written on a paper.

(Numbers can start with 1 or more zeros)

Two numbers are considered equivalent if a number after turning the paper upside down is the same as the other number.

For example: $\displaystyle 0698161$ is equivalent with $\displaystyle 1618690$. (Because 0,1,6,8,9 give the numbers 0,1,9,8,6 after turning the paper upside down.)

Determine how many not-equivalent numbers there are.

Any ideas?