How many 50($=n$) digit strings($=f(n)$) composed of only zeros and ones are there such that all "ones" should be in groups of at least 3(The grouping should be explicit), if they occur and must be separated by atleast one "zero".

Valid Examples:
$$(111)0(111),\;\;\;(1111)00(111)0(11111)0(111)000$$
InValid Examples:
$$(111)(11),\;\;(111)(111),\;\;(111)0(11)$$

It is easy to find it by explicitly writing for lower n. Also it seems that $f(n)$ follows recursion but I can't write it.

I also tried using stars and bars with no progress.

An Explanatory Example:
$$f(7)=17$$
$$\begin{array}{|c|c|c|c|}\hline 1&0000000&10&00(1111)0\\2&(111)0000&11&000(1111)\\3&0(111)000&12&0(1111)00\\4&00(111)00&13&00(1111)0\\5&000(111)0&14&000(1111)\\6&0000(111)&15&(11111)00\\7&(111)0(111)&16&0(11111)0\\8&(1111)000&17&1111111\\9&0(1111)00&&\\\hline\end{array}$$