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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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