Over at Code Golf Stack Exchange, I put up a challenge asking people to count, among other things, the number of ways to take an $n$-cube and color $k$ (connected) edges up to isometries of the $n$-cube. Let's call this number $C(n,k)$.
For example, when $n=3$ (the ordinary cube) and $k=4$, $C(3,4) = 4$ as there are four such colorings. 
I'm particularly interested in computing $C(n,n)$, the case where $n=k$, because $C(n+1,k) = C(n,k)$ for $k \leq n$ (because you can just project down a dimension), so understanding this case illuminates the limiting case as $n$ goes to infinity.
I've computed the first few terms, for $n = k \leq 6$, $$ \begin{align} C(1,1) &= 1, \\ C(2,2) &= 1, \\ C(3,3) &= 3, \\ C(4,4) &= 7, \\ C(5,5) &= 27, \text{ and} \\ C(6,6) &= 121. \end{align} $$ It's computationally expensive to determine $C(7,7)$, but it's running on my machine now.
Looking this up on OEIS, it appears this nearly matches sequence A062363, that is, $C(n,n) = A062363(n-1)$ for $2 \leq n \leq 6$.
I don't have any reason a priori to expect the sequence I've described to be related to the definition of A062363, to be especially nice, or even to be in the OEIS at all.
Does the OEIS sequence actually match the sequence that I'm looking at? Or is this just a coincidence?
The OEIS sequence did not match the next term, so the matching terms were just coincidental. $$ C(7,7) = 751 \neq A062363(6) = 729. $$