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
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.

(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.