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### sequence of functions

How do I define a sequence of functions in Sage?

I'd like to do something like

f(0)(a, b) = a * b
f(n)(a, b) = a + b * f(n-1)(a+b, a-b)


Such that when I use it, I could e.g. solve for x in

f(3)(x, x+1) = 1