Correct, they are for storing data. It sounds like you are trying to use endless lines of C++ code to "encode" your sequences instead of treating the sequences as what they are: data, not program. They may seem too complex to you to be represented as data, and that's why you are taking the approach you have.
You will have seen, in videos, perhaps in real life, fairground organs, pianolas (player pianos), even Jacquard looms. The mechanisms inside these machines are not complex enough to have multiple pieces of complex music or woven patterns built into their mechanisms. The sequences within the music or patterns are encoded on drums or lengths of paper. The mechanism reads the data from the drum/paper and executes the sequences. Even nature uses the same technique: DNA. That's what you need to do with your light sequences.
Here's what I suggest: there are some very clever chaps and ladies on this forum. I'm not so bad myself. So how about giving us an example sequence. Not too long, but not a short one either. Let's see if we can invent a way to reproduce that sequence using less flash memory than your current method, or a way to express it as data which can be stored in a file on an SD card.