User blog comment:QuasarBooster/Fibonacci/Lucas Sequence Extentions?/@comment-2033667-20150730151541/@comment-2033667-20150801034303

I tried to analyze the U^2 one and didn't really get anywhere. I had an idea of considering some continuous generalization of U a la Binet's formula, and then looking at its derivative, which has $$U'(n) = U'(n - 1) + 2 U'(n - 2) U(n - 2)$$. So it becomes a weird system of differential equations that probably has no analytic solution

We can do this with the Q sequence too: $$Q'(n) = Q'(n - Q(n - 1))(1 - Q'(n - 1)) + Q'(n - Q(n - 2))(1 - Q'(n - 2))$$. wheeeeee we have accomplished nothing