On Sequences Gn Satisfying
Gn = (d+2)Gn-1
- Gn-2
Ricky X. F. Chen
Center for Combinatorics
LPMC
Nankai University
Tianjin, 300071
P. R. China
Louis W. Shapiro
Howard University
Washington, DC 20059
USA
Abstract:
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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