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

Sequences That Satisfy a(n-a(n))=0

Nate Kube and Frank Ruskey
Department of Computer Science
University of Victoria
Victoria, British Columbia V8W 3P6

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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(Concerned with sequences A000108 A000110 A000248 A001263 A006318 A008277 A060693 A098568 and A098569 .)

Received March 28 2005; revised version received October 24 2005. Published in Journal of Integer Sequences, October 24 2005.

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