Jason (jcreed) wrote,

Man, if only there were a nice analytic functional operator Δx that satisfied the recurrence

Δx(k + xf) = k2 + xΔx(f)

(assuming f is a formal power series over x) then I could express the generating function for the number of AVL trees of height n by (omitting all the subscript xs for brevity)

f = x(Δf + Δ((1+x)f) + Δ((1-x)f))

It's also too bad Δ doesn't seem to be linear or homomorphic on products or anything else nice like that.
Tags: generating functions

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