consider a 2d "counting" function given by the $(x,y)$ points/pairs:
ie $x$ increments in each pair, $y$ increments on each row, and there are $n+1$ pairs on each subsequent row.
I did a curve fit of this function and got a close fit to an equation in the form $y=ax ^ b + c$. is there an exact or closed-form formula? have some experience with generating functions/recurrence relations with integer coefficients but this seems to be different. (it does seem to be similar to the Fibonacci sequence...) is there a general theory for generating functions for integer equations but with noninteger (rational, irrational) coefficients? what is a good ref on that?