I am currently thinking about the following problem. https://archive.topcoder.com/ProblemStatement/pm/15306 Using DP, we can easily count the number of distinct subsequences, and by extension the number of distinct strictly increasing subsequences. For example, see this blog post: https://codeforces.net/blog/entry/80464?#comment-667033.

However, I'm unsure on how to extend this idea to count the number of distinct subsequences CONTAINING a strictly increasing sub-subsequence. The difficulty arises in cases like [1,2,3,1,2,3,1,2,3], where to count subsequences like [1,3,2,3] (for L=3 for instance) one needs to somehow skip over the leftmost next occurance of the value 2.

Thanks in advance.