How could you estimate the number of (roughly) grammatically correct (I won't even assume coherent because that would probably be impossible) texts consisting of 1000 words or less?
For example, sentences like "Blue sheep dream of yellow equations furiously" would be allowed but sentences like "I have he eats three conquered" would not.
I'm wondering how many books I'd need to generate for one of them to contain my life story.
Clearly if I brute force it by generating every possible character combination, the number of books would be impractical. However, perhaps if I restrict the texts to only grammatically sensible ones, the number would be a bit more realistic, perhaps not exceeding the size of the internet.
Is anything known about the asymptotic growth of T(n) (the number of grammatically correct texts consisting of up to n words)?