Do the powers in Heroes manifest only once a generation?

The complicated dynamics of who gets what powers is never fully explained. For example, Nathan was the son of two people with powers, but was born without powers, they were granted to him synthetically. Peter's powers, however, came to him naturally. Peter has a variation of his dad's powers.

Claire's powers are also interesting to note. Her mom (and we also find her uncle) can control fire. Her father, Nathan, was synthetically given powers. She was born with the ability to heal quickly.

The only person that has a clear line of inheritance that I can recall is Syler, since his real father was exactly like him.

• Isaac Mendez and Usutu could both paint the future.

• Meredith Gordon and her brother Flint could both create and manipulate fire.

• Daniel Linderman and Ishi Nakamura could both heal others through physical contact.

  (Ishi Nakamura died in the early 1990s and is therefore only seen in flashbacks, which is why she doesn't look the same age as Daniel Linderman, even though they are arguably the same generation)