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For example, Ozone has a double and single bond with at least one free pair of electrons in each oxygen atom. My doubt is whether ozone can have a triple bond and single bond with one oxygen atom without a free pair of electrons.

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$\ce{H4O^{2+}}$ is a counter example to such a rule.

http://pubs.acs.org/doi/abs/10.1021/ja00265a031

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