Ruskey: Sequences that satisfy a(n-a(n)) = 0

Sequences that satisfy a(n-a(n)) = 0

Nate Kube, Department of Computer Science, University of Victoria, Canada.
Frank Ruskey, Department of Computer Science, University of Victoria, Canada.

Abstract:

We explore the properties of some sequences for which a(n-a(n)) = 0. Under the natural restriction that a(n) < n the number of such sequences is a Bell number. Adding other natural restrictions yields sequences counted by the Catalan numbers, the Narayana numbers, the triangle of triangular binomial coefficients, and the Schröder numbers.

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Appears in Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.5, 8 pages.

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