Question: A binary string has 7. k runs if it can be divided into exactly k substrings so that each substring either is all 0 bits

A binary string has 7. k runs if it can be divided into exactly k substrings so that each substring either is all 0 bits or all 1 bits. For instance, the string 00111101000111 has 6 runs since it divides into the substrings 00 1111 0 1 000 111 How many binary strings of length n have exactly k runs?

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