I'd like to find the number of possible partitions of a sentence of $n$ words, and each partition has a max size of $k$ letters. Words cannot be broken in the partition and the order must be retained in the partition. Also, all word length ($w_{i}$) $\leq$ $k$. Trying to get a closed form formula
For example, $k=8$ we can have
the rabit | runs | on the | street
I've tried to break down every word into it's own partition, so I get one way. Then there are n-1 ways to get n-1 partitions. Then for larger values I'm not sure how to guarantee each partition is less than k.
So a simplified example:
$a | b | c | d | e$
For $k = 2$, suppose I remove $2$ separaters:
$a b | c d | e$ ---> this is fine
a | b | c d e ----> this is not
Currently not sure what else to try.