A Combinatorial interpretation of Hofstadter's G-sequence

Details A Combinatorial interpretation of Hofstadter's G-sequence A Combinatorial interpretation of Hofstadter's G-sequence

2011-05-09

arxiv.org/abs/1105.1718v2

Mathematics

Combinatorics

7 pages, 1 figure. Version 2 has some changes to the exposition mostly for clarity

Scientific paper

We give a combinatorial interpretation of a classical meta-Fibonacci sequence defined by G(n) = n - G(G(n-1)) with the initial condition G(1) = 1, which appears in Hofstadter's 'Godel, Escher, Bach: An Eternal Golden Braid'. The interpretation is in terms of an infinite labelled tree. We then show a few corollaries about the behaviour of the sequence G(n) directly from the interpretation.

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