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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