How many binary strings of length $$10$$ are there such that there are no consecutive zeros and an even number of ones?

This problem is shared by Muhammad A.

Details and assumptions

A binary string is a sequence of integers that are $$1$$ or $$0$$. The length of a string refers to the number of integers in it.

As an explicit example, the binary string of length $$3$$ are $$000, 001, 010, 011$$, $$100, 101, 110, 111$$.

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