Journal of Integer Sequences, Vol. 10 (2007), Article 07.8.1

On Sequences Gn Satisfying Gn = (d+2)Gn-1 - Gn-2

Ricky X. F. Chen
Center for Combinatorics
Nankai University
Tianjin, 300071
P. R. China

Louis W. Shapiro
Howard University
Washington, DC 20059


In this note, we study a class of sequences Gn satisfying Gn = (d+2)Gn-1 - Gn-2. Note that the Fibonacci numbers Gn = F2n, n >1 and Gn = F2n+1, n > 0 occur when d=1 with suitable initial conditions. We present a general interpretation for this class of sequences in terms of ordered trees which we count by nodes and outdegrees. Further more, several other related integer sequences are also studied.

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(Concerned with sequences A000045 A001835 A030267 A038731 A052530 A105309 and A119749.)

Received May 3 2007; revised version received July 26 2007. Published in Journal of Integer Sequences, August 2 2007.

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