How many binary cyclic sequences of length $n$ exist, where ones only appear in blocks of length at least $k$? We do not consider sequences that result from each other by a cyclic shift equivalent.
Example: Let $n=6$ and $k=2$, i.e. we have no isolated one. Then
[0,0,0,0,0,0]
[1,1,0,0,0,0] and 5 cyclic shifts of it
[1,1,1,0,0,0] and 5 cyclic shifts of it
[1,1,1,1,0,0] and 5 cyclic shifts of it
[1,1,0,1,1,0] and 2 cyclic shifts of it
[1,1,1,1,1,0] and 5 cyclic shifts of it
[1,1,1,1,1,1]
are all of the 29 possible sequences.
The case $k=2$ is covered by https://oeis.org/A109377