I know that Christoffel coefficients are symmetric, so $\Gamma^i_{jk}=\Gamma^i_{kj}$.
I am asked how many dimensions are there for an N-dimensional metric. There are $N$ choices for $i$, $j$ & $k$; half of these are not counted because of the above equality.
So the number of independent connection coefficients are $2^N/2=2^{N-1}$.
Is this reasoning correct?