MathDB
Weird Recursion - Weird Explicit Formula

Source: BWM 1983, Round 2 - #4

November 6, 2017
recursionalgebraalgebra unsolvedSequence

Problem Statement

Let f(0),f(1),f(2),…f(0), f(1), f(2), \dots be a sequence satisfying f(0) = 0   \text{and}   f(n) = n - f(f(n-1)) for n=1,2,3,…n=1,2,3,\dots. Give a formula for f(n)f(n) such that its value can be immediately computed using nn without having to compute the previous terms.
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