I decided to post what I have been working on, as I have been researching this largely in isolation and would value feedback from the community here. I think the approach is novel, it certainly allows one to compute n rows with fewer lookup operations and I haven't found anything else that proposes this particular method, but there may be an iceberg of knowledge I've only just scratched the surface of here, so I hope the community here can provide some insight and feedback.
This is fantastic work and you've presented it very well. Thanks for the writeup.
Yours is the first response, thank you for the kind words :)
I just had some feedback, and did some more number crunching which revealed this is not O(n) but still O(n^2) - I have modifed the article accordingly but will leave it up as the algorithm still provides significant improvements in efficiency for larger numbers of rows.