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That example includes misinformation (the expression given for the fibonacci sequence is not closed-form). The actual closed-form expression for F_n is (phi^n - (1-phi)^n)/sqrt(5), where phi and 1-phi are the solutions to the quadratic equation x^2 = x+1.

Well, I didn't write it, but if you want to argue with the mathematicians over on the typst discord, you can do that.