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H-O-H (water), H-O-O-H (hydrogen peroxide), H-O-O-O-H, H-O-O-O-O-H, etc.
This is analogous to hydrocarbon chains, methane, ethane, propane, butane, etc.
Note the Hydroxygen Chains satisfy 2 covalent bonds for every oxygen atom, just as every Hydrocarbon Chain satisfies 4 covalent bonds for every carbon atom. Yet the oxygen chains seem unstable. Why?
I can't imagine it has anything to do with shells deeper than p. And carbon and oxygen are very close together on the same row, so it would appear the valence shells are the same and thus governed by the same laws.
I'm also aware of those weird exceptions, Ozone and Red Oxygen. Maybe that has something to do with it, but I don't know how those bonds work either.
I also saw this related question. It just asks if they're possible. I didn't see any explanation about why they're unstable.