Muhammad's strings

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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