29 May 2013 Entropy estimation and Fibonacci numbers
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We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 − 1, where Fm is a Fibonacci number.
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Evgeniy A. Timofeev, Evgeniy A. Timofeev, Alexei Kaltchenko, Alexei Kaltchenko, "Entropy estimation and Fibonacci numbers", Proc. SPIE 8750, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XI, 875016 (29 May 2013); doi: 10.1117/12.2016140; https://doi.org/10.1117/12.2016140

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